Question

which exponential function is represented by the logarithmic function $log_{4}g(x)=x+3$?
$\bigcirc$ $g(x)=3cdot4^{x}$
$\bigcirc$ $g(x)=4^{3x}$
$\bigcirc$ $g(x)=4cdot x^{3}$
$\bigcirc$ $g(x)=4^{x+3}$

Explanation:

Step1: Use logarithm to exponent rule

Recall that $\log_b a = c$ converts to $a = b^c$. Here, $b=4$, $a=g(x)$, $c=x+3$.
$$g(x) = 4^{x+3}$$

Step2: Match with options

Compare the derived function to the given choices.

Answer:

$g(x) = 4^{x+3}$