Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Algebra 2
Convert between exponential and logarithmic form: all bases
Consider the equation
0.5
⋅
1
0
8
t
=
73
0.5 \cdot 10^{8 t}=73
0.5
⋅
1
0
8
t
=
73
.
\newline
Solve the equation for
t
t
t
. Express the solution as a logarithm in base
−
10
-10
−
10
.
\newline
t
=
t=
t
=
\newline
□
\square
□
\newline
Approximate the value of
t
t
t
. Round your answer to the nearest thousandth.
\newline
t
≈
t \approx
t
≈
Get tutor help
\sqrt{\(5\)}\times\(10(
3
3
3
,
2
2
2
)\times
4
4
4
(
−
1
-1
−
1
,
4
4
4
)
Get tutor help
3.5
(
x
+
2.2
)
2
+
3.5
(
y
−
11.1
)
2
−
21
=
0
3.5(x+2.2)^{2}+3.5(y-11.1)^{2}-21=0
3.5
(
x
+
2.2
)
2
+
3.5
(
y
−
11.1
)
2
−
21
=
0
\newline
The given equation represents a circle in the
x
y
x y
x
y
-plane. What is the radius of the circle to the nearest hundredth?
\newline
□
\square
□
Get tutor help
Nit.
\newline
junesk
12
12
12
ors bookmaiks
\newline
Mure Menu Stufi
\newline
DragenFly MAX
\newline
- Drift Hunters
\newline
witlon
\newline
iestion
2
2
2
of
10
10
10
\newline
Write the equation for an exponential function, in the form
y
=
a
×
b
x
y=a \times b^{x}
y
=
a
×
b
x
, whose graph passes throt coordinate points
(
1
,
7.5
)
(1,7.5)
(
1
,
7.5
)
and
(
3
,
16.875
)
(3,16.875)
(
3
,
16.875
)
.
Get tutor help
The population of Los Angeles
P
(
t
)
P(t)
P
(
t
)
(in millions) can be approximated by the logistic growth function
\newline
P
(
t
)
=
3.194
1
+
14.589
e
−
0.052
t
P(t)=\frac{3.194}{1+14.589 e^{-0.052 t}}
P
(
t
)
=
1
+
14.589
e
−
0.052
t
3.194
\newline
where
t
t
t
is the number of years since the year
1900
1900
1900
.
\newline
b. Use this function to approximate the population of Los Angeles on January
1
1
1
,
2016
2016
2016
.
Get tutor help
Solve each equation. Ro
\newline
1
1
1
)
log
2
(
v
−
9
)
+
3.3
=
5.6
\log _{2}(v-9)+3.3=5.6
lo
g
2
(
v
−
9
)
+
3.3
=
5.6
Get tutor help
Consider the equation
−
5
⋅
e
10
t
=
−
30
-5 \cdot e^{10 t}=-30
−
5
⋅
e
10
t
=
−
30
.
\newline
Solve the equation for
t
t
t
. Express the solution as a logarithm in base-
e
e
e
.
\newline
t
=
□
t = \square
t
=
□
\newline
Approximate the value of
t
t
t
. Round your answer to the nearest thousandth.
\newline
t
≈
□
t \approx \square
t
≈
□
\newline
Get tutor help
Consider the equation
14
⋅
1
0
0.5
w
=
100
14 \cdot 10^{0.5 w}=100
14
⋅
1
0
0.5
w
=
100
.
\newline
Solve the equation for
w
w
w
. Express the solution as a logarithm in base-
10
10
10
.
\newline
w
=
□
w = \square
w
=
□
\newline
Approximate the value of
w
w
w
. Round your answer to the nearest thousandth.
\newline
w
≈
□
w \approx \square
w
≈
□
Get tutor help
rac{
5
5
5
}{
6
6
6
} W = rac{
10
10
10
}{
3
3
3
}
Get tutor help
Write the log equation as an exponential equation. You do not need to solve for
x
\mathrm{x}
x
.
\newline
log
(
x
2
+
3
x
−
6
)
=
2
\log \left(x^{2}+3 x-6\right)=2
lo
g
(
x
2
+
3
x
−
6
)
=
2
\newline
Answer:
Get tutor help
Write the log equation as an exponential equation. You do not need to solve for
x
\mathrm{x}
x
.
\newline
ln
(
x
2
+
3
x
−
18
)
=
2
\ln \left(x^{2}+3 x-18\right)=2
ln
(
x
2
+
3
x
−
18
)
=
2
\newline
Answer:
Get tutor help
Write the log equation as an exponential equation. You do not need to solve for
x
\mathrm{x}
x
.
\newline
ln
(
x
2
−
2
x
+
7
)
=
9
5
\ln \left(x^{2}-2 x+7\right)=\frac{9}{5}
ln
(
x
2
−
2
x
+
7
)
=
5
9
\newline
Answer:
Get tutor help
Write the log equation as an exponential equation. You do not need to solve for
x
\mathrm{x}
x
.
\newline
ln
(
x
2
+
4
x
+
11
)
=
2
\ln \left(x^{2}+4 x+11\right)=2
ln
(
x
2
+
4
x
+
11
)
=
2
\newline
Answer:
Get tutor help
Write the log equation as an exponential equation. You do not need to solve for
x
\mathrm{x}
x
.
\newline
log
5
(
x
2
−
2
x
+
20
)
=
5
x
\log _{5}\left(x^{2}-2 x+20\right)=5 x
lo
g
5
(
x
2
−
2
x
+
20
)
=
5
x
\newline
Answer:
Get tutor help
Write the log equation as an exponential equation. You do not need to solve for
x
\mathrm{x}
x
.
\newline
ln
(
2
x
+
5
)
=
x
\ln (2 x+5)=x
ln
(
2
x
+
5
)
=
x
\newline
Answer:
Get tutor help
rac{
2354234
2354234
2354234
}{
625
625
625
}
Get tutor help
what is
4
×
12
4\times12
4
×
12
raised to
4
×
9
4 \times9
4
×
9
raised to
3
÷
27
×
8
3 \div27 \times8
3
÷
27
×
8
raised to
2
×
6
2 \times 6
2
×
6
raised to
3
3
3
in exponential form
Get tutor help
3
3
3
. (
6
6
6
pts) Use logarithmic differentiation to find the derivative of
\newline
y
=
(
10
x
2
+
1
)
cos
x
y=\left(10 x^{2}+1\right)^{\cos x}
y
=
(
10
x
2
+
1
)
c
o
s
x
Get tutor help
log
(
5
x
−
5
)
5
+
log
(
x
−
1
)
2
125
>
2
\log _{(5 x-5)} 5+\log (x-1)^{2} 125>2
lo
g
(
5
x
−
5
)
5
+
lo
g
(
x
−
1
)
2
125
>
2
Get tutor help
log
5
x
−
5
5
+
log
(
x
−
1
)
2
125
>
2
\log _{5 x-5} 5+\log _{(x-1)^{2}} 125>2
lo
g
5
x
−
5
5
+
lo
g
(
x
−
1
)
2
125
>
2
Get tutor help
y
=
log
2
(
4
x
2
−
5
x
+
1
)
y=\log_{2}(4x^{2}-5x+1)
y
=
lo
g
2
(
4
x
2
−
5
x
+
1
)
Get tutor help
Write
6
5
=
7776
6^{5}=7776
6
5
=
7776
in logarithmic form
\newline
(A)
log
6
5
=
7776
\log_{6}5=7776
lo
g
6
5
=
7776
\newline
(B)
log
6
7776
=
5
\log_{6}7776=5
lo
g
6
7776
=
5
\newline
(C)
log
5
6
=
7776
\log_{5}6=7776
lo
g
5
6
=
7776
\newline
(D)
log
5
7776
=
6
\log_{5}7776=6
lo
g
5
7776
=
6
Get tutor help
Write an exponential function in the form
y
=
a
b
x
y=a b^{x}
y
=
a
b
x
that goes through the points
(
0
,
14
)
(0,14)
(
0
,
14
)
and
(
7
,
1792
)
(7,1792)
(
7
,
1792
)
.
\newline
Answer:
Get tutor help
log
81
3
=
\log _{81} 3=
lo
g
81
3
=
Get tutor help
log
4
4
=
\log _{4} 4=
lo
g
4
4
=
Get tutor help
log
10
1
,
000
=
\log _{10} 1,000=
lo
g
10
1
,
000
=
Get tutor help
log
2
256
=
\log _{2} 256=
lo
g
2
256
=
Get tutor help
log
4
64
=
\log _{4} 64=
lo
g
4
64
=
Get tutor help
Rewrite the following in the form
log
(
c
)
\log (c)
lo
g
(
c
)
.
\newline
log
(
2
)
+
log
(
2
)
\log (2)+\log (2)
lo
g
(
2
)
+
lo
g
(
2
)
Get tutor help
log
10
1
,
000
,
000
=
\log _{10} 1,000,000=
lo
g
10
1
,
000
,
000
=
Get tutor help
log
3
243
=
\log _{3} 243=
lo
g
3
243
=
Get tutor help
log
10
10
,
000
=
\log _{10} 10,000=
lo
g
10
10
,
000
=
Get tutor help
log
2
4
=
\log _{2} 4=
lo
g
2
4
=
Get tutor help
log
5
625
=
\log _{5} 625=
lo
g
5
625
=
Get tutor help
log
8
512
=
\log _{8} 512=
lo
g
8
512
=
Get tutor help
log
2
128
=
\log _{2} 128=
lo
g
2
128
=
Get tutor help
Of all eligible voters in your county,
70
%
70 \%
70%
are currently registered to vote.
\newline
A recent poll predicts that the relationship between
V
V
V
, the percentage of all eligible voters who are registered to vote, and
t
t
t
, the number of years from now will be modeled by the following equation.
\newline
V
=
100
−
30
⋅
e
−
0.04
t
V=100-30 \cdot e^{-0.04 t}
V
=
100
−
30
⋅
e
−
0.04
t
\newline
In how many years will
80
%
80 \%
80%
of all eligible voters in your county be registered to vote?
\newline
Give an exact answer expressed as a natural logarithm.
\newline
years
Get tutor help
Noah borrows
$
2000
\$ 2000
$2000
from his father and agrees to repay the loan and any interest determined by his father as soon as he has the money.
\newline
The relationship between the amount of money,
A
A
A
, in dollars that Noah owes his father (including interest), and the elapsed time,
t
t
t
, in years, is modeled by the following equation.
\newline
A
=
2000
e
0.1
t
A=2000 e^{0.1 t}
A
=
2000
e
0.1
t
\newline
How long did it take Noah to pay off his loan if the amount he paid to his father was equal to
$
2450
\$ 2450
$2450
? Give an exact answer expressed as a natural logarithm.
Get tutor help
A scientist measures the initial amount of Carbon
−
14
-14
−
14
in a substance to be
25
25
25
grams.
\newline
The relationship between
A
A
A
, the amount of Carbon
−
14
-14
−
14
remaining in that substance, in grams, and
t
t
t
, the elapsed time, in years, since the initial measurement is modeled by the following equation.
\newline
A
=
25
e
−
0.00012
t
A=25 e^{-0.00012 t}
A
=
25
e
−
0.00012
t
\newline
In how many years will the substance contain exactly
20
20
20
grams
(
g
)
(\mathrm{g})
(
g
)
of Carbon
−
14
-14
−
14
?
\newline
Give an exact answer expressed as a natural logarithm.
\newline
years
Get tutor help
Write the expression in exponential form.
\newline
9
×
9
×
9
×
9
×
9
×
9
×
9
=
9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9=
9
×
9
×
9
×
9
×
9
×
9
×
9
=
Get tutor help
Write the expression in exponential form.
\newline
7
×
7
×
7
×
7
×
7
×
7
=
7 \times 7 \times 7 \times 7 \times 7 \times 7=
7
×
7
×
7
×
7
×
7
×
7
=
Get tutor help
Write the expression in exponential form.
\newline
6
×
6
×
6
×
6
×
6
=
6 \times 6 \times 6 \times 6 \times 6=
6
×
6
×
6
×
6
×
6
=
Get tutor help
Write the expression in exponential form.
\newline
8
×
8
×
8
×
8
=
8 \times 8 \times 8 \times 8=
8
×
8
×
8
×
8
=
Get tutor help
Write the logarithmic equation in exponential form.
\newline
log
10
100
=
2
\log_{10}100 = 2
lo
g
10
100
=
2
\newline
1
0
2
=
‾
10^2 = \underline{\hspace{2em}}
1
0
2
=
Get tutor help
