Question

What is the solution to the equation below? log, X=4

Answer 1

To solve the logarithmic equation, you have to pass it to exponential form, following the rule:

`log_b(x)=a\text{ }→\text{ }b^a=x`

Considering the given logarithmic equation:

`log_8(x)=4`

- The base of the logarithm will be the base of the exponential value, in this case, b=8.

- The result of the logarithm corresponds to the exponential index, in this case, a=4

Rewrite the expression:

`log_8(x)=4\text{ }→\text{ }x=8^4`

Solve the exponent to find the value of x:

`\begin{gathered} x=8^4 \\ x=4096 \end{gathered}`

The correct answer is x=4096 (option B)