Question

In the following exercises, convert each logarithmic equation to exponential form.

$7={\log }_2\left(128\right)$

Short answer

The exponential form is $2^7=128$.

Step-by-step solution

Step 1. Concept used

Consider the logarithmic form $7={\log }_2\left(128\right)$.

The logarithmic form $y={\log }_a\left(x\right)$is equivalent to exponential form

$a^y=x$.

Step 2. Write in exponential form

Comparing $7={\log }_2\left(128\right)$with the standard form,

$y={\log }_a\left(x\right)$we have

$$\begin{gathered} y=7 \\ a=2 \\ x=128 \end{gathered}$$

So substituting the values in standard exponential form $a^y=x$we get

$$\begin{gathered} a^y=x \\ {2}^7=128 \end{gathered}$$