Write the logarithmic equation in exponential form. log100 = 2 10^2 = ____

Identify base, logarithm result, and number: Identify the base (b), the logarithm result (y), and the number (x) from the logarithmic equation log100 = 2. In a logarithmic equation of the form log_b(x) = y, b is the base, x is the number, and y is the result. Here, the base is assumed to be 10 because it is not specified (common logarithm), so b = 10, x = 100, and y = 2.Convert to exponential form: Convert the logarithmic equation to exponential form using the relationship b^y = x. Substitute b = 10, y = 2, and x = 100 into the equation to get 10^2 = 100.Check the calculation: Check the calculation to ensure that raising the base to the power of the result gives the number. 10^2 = 10 * 10 = 100, which matches the number x in the logarithmic equation.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write the logarithmic equation in exponential form. $\newline$ $\log_{10}100 = 2$ $\newline$ $10^2 = \underline{\hspace{2em}}$

View step-by-step help

Home

Math Problems

Algebra 2

Convert between exponential and logarithmic form: all bases

Full solution

Q. Write the logarithmic equation in exponential form.

\newline

\log_{10}100 = 2

\newline

10^2 = \underline{\hspace{2em}}

Identify base, logarithm result, and number: Identify the base (), the logarithm result (), and the number () from the logarithmic equation () = . In a logarithmic equation of the form _() = , is the base, is the number, and is the result. Here, the base is assumed to be because it is not specified (common logarithm), so = , = , and = .
Convert to exponential form: Convert the logarithmic equation to exponential form using the relationship $b^y = x$ . $\newline$ Substitute $b = 10$ , $y = 2$ , and $x = 100$ into the equation to get $10^2 = 100$ .
Check the calculation: Check the calculation to ensure that raising the base to the power of the result gives the number. $10^2 = 10 \times 10 = 100$ , which matches the number $x$ in the logarithmic equation.