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Welcome to Bytelearn!
Let’s check out your problem:
Find the value of
x
x
x
that solves the equation
ln
(
x
−
3
)
−
3
ln
4
=
ln
10
\ln (x-3)-3 \ln 4=\ln 10
ln
(
x
−
3
)
−
3
ln
4
=
ln
10
.
\newline
Answer:
x
=
x=
x
=
View step-by-step help
Home
Math Problems
Algebra 2
Solve linear equations
Full solution
Q.
Find the value of
x
x
x
that solves the equation
ln
(
x
−
3
)
−
3
ln
4
=
ln
10
\ln (x-3)-3 \ln 4=\ln 10
ln
(
x
−
3
)
−
3
ln
4
=
ln
10
.
\newline
Answer:
x
=
x=
x
=
Write Equation:
Write down the given equation.
\newline
We have the equation
ln
(
x
−
3
)
−
3
ln
4
=
ln
10
\ln(x-3) - 3\ln 4 = \ln 10
ln
(
x
−
3
)
−
3
ln
4
=
ln
10
.
Simplify Logarithms:
Use the property of logarithms that
ln
(
a
b
)
=
b
⋅
ln
(
a
)
\ln(a^b) = b\cdot\ln(a)
ln
(
a
b
)
=
b
⋅
ln
(
a
)
to simplify the term with
ln
4
\ln 4
ln
4
.
ln
(
x
−
3
)
−
ln
(
4
3
)
=
ln
10
\ln(x-3) - \ln(4^3) = \ln 10
ln
(
x
−
3
)
−
ln
(
4
3
)
=
ln
10
Recognize Value:
Recognize that
4
3
4^3
4
3
is
64
64
64
.
\newline
ln
(
x
−
3
)
−
ln
(
64
)
=
ln
10
\ln(x-3) - \ln(64) = \ln 10
ln
(
x
−
3
)
−
ln
(
64
)
=
ln
10
Combine Logarithms:
Use the property of logarithms that
ln
(
a
)
−
ln
(
b
)
=
ln
(
a
b
)
\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)
ln
(
a
)
−
ln
(
b
)
=
ln
(
b
a
)
to combine the logarithms on the left side.
\newline
ln
(
x
−
3
64
)
=
ln
10
\ln\left(\frac{x-3}{64}\right) = \ln 10
ln
(
64
x
−
3
)
=
ln
10
Set Equal:
If
ln
(
a
)
=
ln
(
b
)
\ln(a) = \ln(b)
ln
(
a
)
=
ln
(
b
)
, then
a
=
b
a = b
a
=
b
. So, set the inside of the logarithms equal to each other.
x
−
3
64
=
10
\frac{x-3}{64} = 10
64
x
−
3
=
10
Multiply by
64
64
64
:
Solve for
x
x
x
by multiplying both sides of the equation by
64
64
64
.
x
−
3
=
10
×
64
x - 3 = 10 \times 64
x
−
3
=
10
×
64
Calculate Result:
Calculate
10
×
64
10 \times 64
10
×
64
.
\newline
x
−
3
=
640
x - 3 = 640
x
−
3
=
640
Isolate x:
Add
3
3
3
to both sides to isolate
x
x
x
.
\newline
x
=
640
+
3
x = 640 + 3
x
=
640
+
3
Add
3
3
3
:
Calculate
640
+
3
640 + 3
640
+
3
.
\newline
x
=
643
x = 643
x
=
643
More problems from Solve linear equations
Question
3
n
2
=
27
3 n^{2}=27
3
n
2
=
27
\newline
What are the solutions to the given equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
n
=
3
n=\sqrt{3}
n
=
3
\newline
(B)
n
=
3
n=3
n
=
3
\newline
(C)
n
=
−
3
n=-\sqrt{3}
n
=
−
3
and
n
=
3
n=\sqrt{3}
n
=
3
\newline
(D)
n
=
−
3
n=-3
n
=
−
3
and
n
=
3
n=3
n
=
3
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Question
If
6
=
3
x
6=3 x
6
=
3
x
, what is the value of
x
x
x
?
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Posted 7 months ago
Question
If
9
=
9
x
9=9 x
9
=
9
x
, what is the value of
x
x
x
?
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Question
1
2
c
2
+
3
c
=
1
\frac{1}{2} c^{2}+3 c=1
2
1
c
2
+
3
c
=
1
\newline
Let
c
=
f
c=f
c
=
f
and
c
=
g
c=g
c
=
g
be the solutions to the given equation. If
f
>
g
f>g
f
>
g
, which of the following is the value of
f
f
f
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
3
+
2
-3+\sqrt{2}
−
3
+
2
\newline
(B)
−
3
+
11
-3+\sqrt{11}
−
3
+
11
\newline
(C)
3
+
2
3+\sqrt{2}
3
+
2
\newline
(D)
3
+
11
3+\sqrt{11}
3
+
11
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Posted 1 year ago
Question
Find the value of
x
x
x
that solves the equation
ln
(
x
−
3
)
=
1
+
ln
2
\ln (x-3)=1+\ln 2
ln
(
x
−
3
)
=
1
+
ln
2
.
\newline
Answer:
Get tutor help
Posted 1 year ago
Question
Find the value of
x
x
x
that solves the equation
ln
(
x
−
1
)
+
ln
5
=
2
\ln (x-1)+\ln 5=2
ln
(
x
−
1
)
+
ln
5
=
2
.
\newline
Answer:
Get tutor help
Posted 1 year ago
Question
Find the value of
x
x
x
that solves the equation
ln
(
x
+
3
)
−
ln
2
=
0
\ln (x+3)-\ln 2=0
ln
(
x
+
3
)
−
ln
2
=
0
.
\newline
Answer:
Get tutor help
Posted 1 year ago
Question
Find the value of `x`
\newline
6
x
+
32
=
8
x
−
8
6x+32=8x-8
6
x
+
32
=
8
x
−
8
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Posted 1 year ago
Question
Aiden has
$
200
\$200
$200
with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get
40
40
40
hats. If Aiden purchases only t-shirts, he will get
80
80
80
t-shirts. Which of the following best models the relationship between the number of hats,
h
h
h
, and the number of t-shirts,
t
t
t
, that Aiden could purchase with this money?
\newline
Choose
1
1
1
answer:
\newline
(A)
40
h
+
80
t
=
400
40h+80t=400
40
h
+
80
t
=
400
\newline
(B)
80
h
+
40
t
=
200
80h+40t=200
80
h
+
40
t
=
200
\newline
(C)
5
h
+
2.5
t
=
200
5h+2.5t=200
5
h
+
2.5
t
=
200
\newline
(D)
2.5
h
+
5
t
=
200
2.5h+5t=200
2.5
h
+
5
t
=
200
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Posted 1 year ago
Question
You pick a card at random, put it back, and then pick another card at random.
\newline
4
4
4
\newline
5
5
5
\newline
6
6
6
\newline
7
7
7
\newline
What is the probability of picking a number greater than
5
5
5
and then picking a
4
4
4
?
\newline
Write your answer as a percentage.
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Posted 7 months ago
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