Solve the exponential equation. Express the solution set in terms of natural logarithms.
-$$10 ^ { x } = 4.04$$
A) $0.61$
B) $10,964.78$
C) $1.4$
D) $40.4$

Question

Quizplus · Accepted Answer

To solve the equation $10^x = 4.04$, take the natural logarithm of both sides: $\ln(10^x) = \ln(4.04)$. This simplifies to $x\ln(10) = \ln(4.04)$, and since $\ln(10)$ is a constant, you can solve for $x$ by dividing both sides by $\ln(10)$, resulting in $x = \frac{\ln(4.04)}{\ln(10)}$, which simplifies to approximately 0.61 when calculated.

Solve the Exponential Equation 10x=4.0410 ^ { x } = 4.0410x=4.04

Solve the Exponential Equation $10 ^ { x } = 4.04$