Problem

Solve for $x$
\[
\ln (5 x-6)=\ln 5
\]
\[
x=
\]

Answer

Expert–verified
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Answer

The solution to the equation is \(\boxed{\frac{11}{5}}\)

Steps

Step 1 :The natural logarithm function is a one-to-one function, which means that if \(\ln a = \ln b\), then \(a = b\). So, we can set the arguments of the two logarithms equal to each other and solve for \(x\).

Step 2 :\(5x - 6 = 5\)

Step 3 :Solving for \(x\), we get \(x = \frac{11}{5}\)

Step 4 :The solution to the equation is \(\boxed{\frac{11}{5}}\)

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