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Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
-$$4^{ ( x - 1 )} = 19$$
A) $\{ 5.75 \}$
B) $\{ 3.12 \}$
C) $\{ 1.12 \}$
D) $\{ 2.26 \}$

Question

Quizplus · Accepted Answer

To solve the equation $4^{(x - 1)} = 19$, we first take the logarithm of both sides. Using the logarithm base 10 for simplicity, we get $\log(4^{(x - 1)}) = \log(19)$. Applying the logarithm power rule, this becomes $(x - 1) \log(4) = \log(19)$. Solving for $x$, we find $x = \frac{\log(19)}{\log(4)} + 1$. Using a calculator to compute this gives $x \approx 3.12$.

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