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Exercise

$\ln x=2.5$

Step-by-step Solution

1

Take the variable outside of the logarithm

$e^{\ln\left(x\right)}=e^{2.5}$
2

Simplifying the logarithm

$x=e^{2.5}$

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

$x=e^{2.5}$

Final answer to the exercise

$x=e^{2.5}$

Exact Numeric Answer

$x=12.1825$

Try other ways to solve this exercise

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Similar Questions Solved

$\log\left(x\right)=3$

$2log\left(x\right)-log\left(x+6\right)=0$

$\log_3\left(x+4\right)+\log_3\left(x-4\right)=2$

$\log\left(4X^2\right)=128$

$\log_x\left(64\right)=3$

$\log_2\left(x-2\right)+\log_2\left(x+1\right)=2$

$2\cdot log\left(x\right)-1\cdot log\left(x+6\right)=0$

Main Topic: Logarithmic Equations

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

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