Solve the logarithmic equation.
\[
\ln (9 x+8)-\ln x=\ln 10
\]

What is the equivalent algebraic equation that must be solved?
A. $(9 x+8) x=e^{10}$
B. $\frac{9 x+8}{x}=10$
C. $\frac{9 x+8}{x}=e^{10}$
D. $(9 x+8) x=10$

Answer

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Answer

So, the final answer is $\boxed{\frac{9 x+8}{x}=10}$

Steps

Step 1 ：$\ln (9 x+8)-\ln x=\ln 10$

Step 2 ：Using the properties of logarithms, rewrite the equation as $\ln \left(\frac{9 x+8}{x}\right)=\ln 10$

Step 3 ：Since the natural logarithm is a one-to-one function, equate the arguments of the logarithms to get the equivalent algebraic equation: $\frac{9 x+8}{x}=10$

Step 4 ：So, the final answer is $\boxed{\frac{9 x+8}{x}=10}$

Solve the logarithmic equation.\[\ln (9 x+8)-\ln x=\ln 10\] What is the equivalent algebraic equation that must be solved?A. $(9 x+8) x=e^{10}$B. $\frac{9 x+8}{x}=10$C. $\frac{9 x+8}{x}=e^{10}$D. $(9 x+8) x=10$

Answer

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Solve the logarithmic equation.
\[
\ln (9 x+8)-\ln x=\ln 10
\]

What is the equivalent algebraic equation that must be solved?
A. $(9 x+8) x=e^{10}$
B. $\frac{9 x+8}{x}=10$
C. $\frac{9 x+8}{x}=e^{10}$
D. $(9 x+8) x=10$