Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Find the numerical value of the log expression. {:[log a=7quad log b=4quad log c=6],[log ((b^(8))/(a^(6)c^(5)))]:} Answer:$

Find the numerical value of the log expression. $\newline$ $\begin{array}{c} \log a=7 \quad \log b=4 \quad \log c=6 \\ \log \frac{b^{8}}{a^{6} c^{5}} \end{array}$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Quotient property of logarithms

Full solution

Q. Find the numerical value of the log expression.

\newline

\begin{array}{c} \log a=7 \quad \log b=4 \quad \log c=6 \\ \log \frac{b^{8}}{a^{6} c^{5}} \end{array}

\newline

Answer:

Apply Quotient Rule: Using the given values for $\log a$ , $\log b$ , and $\log c$ , we need to evaluate the expression $\log\left(\frac{b^8}{a^6c^5}\right)$ . We can use the properties of logarithms to simplify the expression. $\newline$ First, apply the quotient rule of logarithms, which states that $\log\left(\frac{a}{b}\right) = \log(a) - \log(b)$ . $\newline$ \log\left(\frac{b^\(8\)}{a^\(6\)c^\(5\)}\right) = \log(b^\(8) - \log(a^ $6$ c^ $5$ )
Apply Product Rule: Next, apply the product rule of logarithms to the term $\log(a^6c^5)$ , which states that $\log(ab) = \log(a) + \log(b)$ . $\newline$ $\log(a^6c^5) = \log(a^6) + \log(c^5)$
Apply Power Rule: Now, apply the power rule of logarithms to each term, which states that $\log(a^n) = n\log(a)$ . $\newline$ $\log(b^8) = 8\log(b)$ $\newline$ $\log(a^6) = 6\log(a)$ $\newline$ $\log(c^5) = 5\log(c)$
Substitute Given Values: Substitute the given values for $\log a$ , $\log b$ , and $\log c$ into the expression. $\newline$ $\log(b^8) - (\log(a^6) + \log(c^5)) = 8\cdot\log(b) - (6\cdot\log(a) + 5\cdot\log(c))$ $\newline$ $= 8\cdot4 - (6\cdot7 + 5\cdot6)$
Perform Arithmetic Operations: Perform the arithmetic operations. $\newline$ $= 32 - (42 + 30)$ $\newline$ $= 32 - 72$ $\newline$ $= -40$

More problems from Quotient property of logarithms

Question

Solve. Write your answer as an integer or a fraction in simplest form.

\newline

5^x=1

\newline

x=

Posted 2 months ago

Question

Steven opened a savings account and deposited

\$100.00

as principal. The account earns

9\%

interest, compounded annually. What is the balance after

5

\newline

Use the formula

A = P(1 + \frac{r}{n})^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years.

\newline

Round your answer to the nearest cent.

\newline

\$

Posted 2 months ago

Question

Use the following function rule to find

f(1)

\newline

f(x) = 12(7)^x + 8

\newline

f(1) =

Posted 1 month ago

Question

The town of Valley View conducted a census this year, which showed that it has a population of

1,800

people. Based on the census data, it is estimated that the population of Valley View will grow by

12\%

\newline

Write an exponential equation in the form

y = a(b)^x

that can model the town population,

y

x

decades after this census was taken.

\newline

Use whole numbers, decimals, or simplified fractions for the values of

a

b

\newline

y =

Posted 2 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = 9^x

\newline

x =

Posted 2 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = e^x

\newline

x =

Posted 1 month ago

Question

Solve. Simplify your answer.

\newline

\log u = 1

\newline

u =

Posted 2 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

\newline

x =

Posted 1 month ago

Question

g(t) = 3^t

change over the interval from

t = 3

t = 4

\newline

\newline

g(t)

3

\newline

g(t)

3

\newline

g(t)

3\%

\newline

g(t)

200\%

Posted 2 months ago

Question

f(x)

6

over every unit interval in

x

f(0) = 0

\newline

Which could be a function rule for

f(x)

\newline

\newline

f(x) = 6^x

\newline

f(x) = 6x

\newline

f(x) = \frac{1}{6^x}

\newline

f(x) = \frac{x}{6}

Posted 2 months ago