Exercise: Write the exponential equation in logarithmic form.
\[
\left(\frac{1}{8}\right)^{-2}=64
\]

Answer

Expert–verified

Hide Steps

Answer

Therefore, the final answer is \(\boxed{\log_{\frac{1}{8}}(64) = -2}\)

Steps

Step 1 ：Given the exponential equation \(\left(\frac{1}{8}\right)^{-2}=64\)

Step 2 ：We can convert this into logarithmic form

Step 3 ：The base of the exponent becomes the base of the logarithm, the result of the exponentiation becomes the argument of the logarithm, and the exponent becomes the value of the logarithm

Step 4 ：So, the logarithmic form of the given equation is \(\log_{\frac{1}{8}}(64) = -2\)

Step 5 ：Therefore, the final answer is \(\boxed{\log_{\frac{1}{8}}(64) = -2}\)

Exercise: Write the exponential equation in logarithmic form.\[\left(\frac{1}{8}\right)^{-2}=64\]

Answer

Popular Problems

Exercise: Write the exponential equation in logarithmic form.
\[
\left(\frac{1}{8}\right)^{-2}=64
\]