The true solution x for the logarithmic equation which is shown below will be 75.
[tex]2 \ln e^{\ln 2x} - \ln e ^{\ln 10} = \ln 30[/tex]
Logarithms are another way of writing exponent. A logarithm with a number base is equal to the other number. It is just the opposite of the exponent function.
The logarithmic equation is given below.
[tex]2 \ln e^{\ln 2x} - \ln e ^{\ln 10} = \ln 30[/tex]
We know that the properties of the logarithm
[tex]e ^{\ln x} = x\\\\a \ln b = \ln b^a\\\\\ln a - \ln b = \ln (\dfrac{a}{b})[/tex]
Then we have
[tex]\begin{aligned} 2 \ln 2x - \ln 10x &= \ln 30\\\\\ln (2x)^2 - \ln 10x &= \ln 30\\\\\ln 4x^2 - \ln 10x &= \ln 30\\\\\ln \dfrac{4x^2 }{10x} &= \ln 30\\\\\ln \dfrac{2x}{5} &= \ln 30 \end{aligned}[/tex]
Taking anti-log, then we have
[tex]\rm \dfrac{2x}{5} = 30\\\\2x \ = 150\\\\x \ \ = 75[/tex]
More about the logarithm link is given below.
https://brainly.com/question/7302008
