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Exercise

$y=e^{\ln\left(81\right)-\ln\left(9\right)}$

Step-by-step Solution

1

Simplify $e^{\left(\ln\left(81\right)-\ln\left(9\right)\right)}$ by applying the properties of exponents and logarithms

$y=81\cdot e^{-\ln\left(9\right)}$
2

Simplify $e^{-\ln\left(9\right)}$ by applying the properties of exponents and logarithms

$y=81\cdot 9^{-1}$

Verify that the solutions obtained are valid in the initial equation

3

The valid solutions to the logarithmic equation are the ones that, when replaced in the original equation, don't result in any logarithm of negative numbers or zero, since in those cases the logarithm does not exist

$y=81\cdot 9^{-1}$

Final answer to the exercise

$y=81\cdot 9^{-1}$

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Main Topic: Logarithmic Equations

Are those equations in which the unknown variable appears within a logarithm.

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