To solve the logarithmic equation, you have to pass it to exponential form, following the rule:
[tex]log_b(x)=a\text{ }→\text{ }b^a=x[/tex]
Considering the given logarithmic equation:
[tex]log_8(x)=4[/tex]
- 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:
[tex]log_8(x)=4\text{ }→\text{ }x=8^4[/tex]
Solve the exponent to find the value of x:
[tex]\begin{gathered} x=8^4 \\ x=4096 \end{gathered}[/tex]
The correct answer is x=4096 (option B)
