Question

find x if 2^5=1/2^x​

Answer 1

Let's solve your equation step-by-step in two methods.

$2^5=\left(\frac{1}{2}\right)^x$

Method 1:

$32=(\frac{1}{2})^x$

Step 1: Flip the equation.

$(\frac{1}{2})^x=32$

Step 2: Solve Exponent.

$(\frac{1}{2})^x=32$

(Take log of both sides)

$log((\frac{1}{2})^{x})=log(32)$

$x*(log(\frac{1}{2}))=log(32)$

$x=\frac{log(32)}{log(\frac{1}{2}) }$

$x=-5$

Method 2:

We have a law of exponent which states ⇒ $a^{-m} = \frac{1}{a^{m}}$

So if $a^{-m} = \frac{1}{a^{m}}$ then we can also say that $a^{m}=\frac{1}{a^{-m}}$

So therefore in the following equation $2^{5}=\frac{1}{2^{-5}}$.

$x=-5$

∴ $x=-5$ in the equation $2^5=\left(\frac{1}{2}\right)^x$.