due: february 20 at 3:35 pm\ngrade: 17%\nnew test grade: 27%\n(type 2)\nconvert log equation to exponential…

due: february 20 at 3:35 pm\ngrade: 17%\nnew test grade: 27%\n(type 2)\nconvert log equation to exponential (numeric)\nexpanding logarithms (level 2)\ncondensing logarithms\nfind growth/decay percentage (level 1)\nquestion\nwrite the logarithmic equation as an exponential equation.\n$log_{2}left(\frac{1}{sqrt{8}}\right)=-\frac{3}{2}$\nanswer attempt 1 out of 2\nsubmit answer

due: february 20 at 3:35 pm\ngrade: 17%\nnew test grade: 27%\n(type 2)\nconvert log equation to exponential (numeric)\nexpanding logarithms (level 2)\ncondensing logarithms\nfind growth/decay percentage (level 1)\nquestion\nwrite the logarithmic equation as an exponential equation.\n$log_{2}left(\frac{1}{sqrt{8}}\right)=-\frac{3}{2}$\nanswer attempt 1 out of 2\nsubmit answer

Answer

Explanation:

Step1: Recall log-exponential conversion rule

For $\log_b(x) = y$, the exponential form is $b^y = x$

Step2: Identify values for conversion

Here, $b=2$, $y=-\frac{3}{2}$, $x=\frac{1}{\sqrt{8}}$

Step3: Substitute into exponential form

$2^{-\frac{3}{2}} = \frac{1}{\sqrt{8}}$

Answer:

$2^{-\frac{3}{2}} = \frac{1}{\sqrt{8}}$