Question

Solve: $3\log x=\log 64$

Short answer

By solving the expression, $3\log x=\log 64$, the value of $x$ is $4$

Step-by-step solution

Step 1. Given

An expression $3\log x=\log 64$

To solve the expression

Step 2. Use the Power Property of logarithm.

Use the Power Property.

$3\log x=\log 64$

$\log x^3=\log 64$

Step 3. Use the One-to-One Property

Use the One-to-One Property, if ${\log }_{a}M={\log }_{a}N$, then $M=N$

$x^3=64$

Step 4. Solve using the Square Root Property.

Solve using the cube Root Property.

$$\begin{gathered} x^3=64 \\ {4}^3=64 \end{gathered}$$

So the value of $x$is $4$

Step 5. To check the solution

Substitute $x=4$in the original equation.

$$\begin{gathered} 3\log \left(4\right)=\log 64 \\ \log {\left(4\right)}^3=\log 64 \\ \log 64=\log 64 \end{gathered}$$

Hence the solution has been checked.