If $\log _{4} x=3$, find the value of $x$ without a calculator.
\[
\mathrm{x}=
\]
(Simplify your answer.)

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The value of x is $\boxed{64}$

Steps

Step 1 ：The question is asking for the value of x given that $\log _{4} x=3$. This is a logarithmic equation. The base of the logarithm is 4 and the result is 3.

Step 2 ：To solve for x, we need to convert the logarithmic equation to an exponential equation. The base of the logarithm becomes the base of the power, the result of the logarithm becomes the exponent, and x is the result of the power.

Step 3 ：base = 4, exponent = 3, so x = $4^3$

Step 4 ：Simplify $4^3$ to get x = 64

Step 5 ：Final Answer: The value of x is $\boxed{64}$

If $\log _{4} x=3$, find the value of $x$ without a calculator.\[\mathrm{x}=\](Simplify your answer.)

Answer

Popular Problems

If $\log _{4} x=3$, find the value of $x$ without a calculator.
\[
\mathrm{x}=
\]
(Simplify your answer.)