Write the exponential equation in logarithmic form. $$e ^ { 9 x } = 10$$
A) $\ln 10 = - 9 x$
B) $\ln 9 = 10 x$
C) $\ln 10 = 9 x$
D)$\ln 10 = \frac { 1 } { 9 } x$
E)$\ln 10 = -\frac { 1 } { 9 } x$

Question

Write the exponential equation in logarithmic form. $$e ^ { 9 x } = 10$$ 
A) $\ln 10 = - 9 x$
B) $\ln 9 = 10 x$
C) $\ln 10 = 9 x$
D)$\ln 10 = \frac { 1 } { 9 } x$
E)$\ln 10 = -\frac { 1 } { 9 } x$

Quizplus · Accepted Answer

Taking the natural logarithm of both sides, we have $$\ln(e^{9x}) = \ln(10)$$ $$9x \ln(e) = \ln(10)$$ Since $\ln(e) = 1$, we can simplify this to $$9x = \ln(10)$$ Dividing both sides by 9, we get $$x = \frac{1}{9} \ln(10)$$ Therefore, the correct choice is $\boxed{\textbf{(C)}}$.

Write the Exponential Equation in Logarithmic Form e9x=10e ^ { 9 x } = 10e9x=10

Write the Exponential Equation in Logarithmic Form $e ^ { 9 x } = 10$