Questions: Solve for x in the equation logx(64)=3

Transcript text: Solve for $x$ in the equation $\log _{x}(64)=3$

Solution

Solution Steps

Step 1: Understand the Equation

The given equation is $\log_{x}(64) = 3$. This is a logarithmic equation where the base is $x$, the argument is 64, and the result is 3.

Step 2: Convert the Logarithmic Equation to an Exponential Equation

The logarithmic equation $\log_{x}(64) = 3$ can be rewritten in its exponential form. The general form of a logarithmic equation $\log_{b}(a) = c$ is equivalent to the exponential equation $b^c = a$.

Thus, we have: \[ x^3 = 64 \]

Step 3: Solve the Exponential Equation

To solve for $x$, we need to find the cube root of 64: \[ x = \sqrt[3]{64} \]

Since $64 = 4^3$, it follows that: \[ x = 4 \]

Final Answer

The solution to the equation $\log_{x}(64) = 3$ is $\boxed{x = 4}$.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >