QuestionSolve the given equation for $x$. $$4^{5 x-3}=45$$

Studdy Solution
Solve for $x$ by first isolating the term with $x$. Divide both sides by $\ln(4)$:
$$5x - 3 = \frac{\ln(45)}{\ln(4)}$$
Next, add 3 to both sides:
$$5x = \frac{\ln(45)}{\ln(4)} + 3$$
Finally, divide by 5 to solve for $x$:
$$x = \frac{1}{5} \left( \frac{\ln(45)}{\ln(4)} + 3 \right)$$
The solution for $x$ is:
$$x = \frac{1}{5} \left( \frac{\ln(45)}{\ln(4)} + 3 \right)$$