Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Express the given expression as an integer or as a fraction in simplest form. log(10^(2)) Answer:$

Express the given expression as an integer or as a fraction in simplest form. $\newline$ $\log \left(10^{2}\right)$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Evaluate logarithms

Full solution

Q. Express the given expression as an integer or as a fraction in simplest form.

\newline

\log \left(10^{2}\right)

\newline

Answer:

Identify base and argument: Identify the base of the logarithm and the argument. $\newline$ The base of the logarithm is $10$ , which is the common logarithm base, and the argument is $10^{2}$ .
Apply logarithm power rule: Apply the logarithm power rule. $\newline$ The power rule of logarithms states that $\log_b(a^n) = n \cdot \log_b(a)$ , where $b$ is the base, $a$ is the argument, and $n$ is the exponent. $\newline$ For our expression, $\log(10^{2})$ can be rewritten as $2 \cdot \log(10)$ .
Evaluate $\log(10)$ : Evaluate $\log(10)$ . $\newline$ Since the base of the logarithm is $10$ and the argument is also $10$ , $\log(10)$ is equal to $1$ because $10^1 = 10$ .
Multiply exponent by log( $10$ ): Multiply the exponent by the value of $\log(10)$ . Now we have $2 \times \log(10)$ which is $2 \times 1$ . This simplifies to $2$ .

More problems from Evaluate logarithms

Question

x

\newline

5^x=1

\newline

\newline

Write your answer in simplest form.

Posted 5 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.

Posted 4 months ago

Question

Use the following function rule to find

f(1)

\newline

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

Posted 5 months 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 8 months ago

Question

x

\newline

7 = 9^x

\newline

Round your answer to the nearest thousandth.

Posted 4 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = e^x

\newline

x =

Posted 7 months ago

Question

Solve. Simplify your answer.

\newline

\log u = 1

\newline

u =

Posted 9 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

\newline

x =

Posted 7 months 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 4 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) = 6x

\newline

f(x) = 6^x

\newline

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

\newline

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

Posted 4 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant