which logarithmic equation has the same solution as $x - 4=2^{3}$?\n$\\log3^{2}=(x - 4)$\n$\\log2^{3}=(x…

which logarithmic equation has the same solution as $x - 4=2^{3}$?\n$\\log3^{2}=(x - 4)$\n$\\log2^{3}=(x - 4)$\n$\\log_{2}(x - 4)=3$\n$\\log_{3}(x - 4)=2$

which logarithmic equation has the same solution as $x - 4=2^{3}$?\n$\\log3^{2}=(x - 4)$\n$\\log2^{3}=(x - 4)$\n$\\log_{2}(x - 4)=3$\n$\\log_{3}(x - 4)=2$

Answer

Explanation:

Step1: Recall the log - exponential conversion

The general conversion rule is if $y = a^x$, then $\log_a y=x$. Given the equation $x - 4=2^3$, comparing with $y = a^x$ where $y=x - 4$, $a = 2$ and $x = 3$.

Step2: Convert to logarithmic form

By the conversion rule, we get $\log_2(x - 4)=3$.

Answer:

C. $\log_2(x - 4)=3$