jisu61hbke

2022-03-21

Solve the equation ${e}^{-2x+1}=13$

armejantm925

Beginner2022-03-22Added 20 answers

Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to perform arithmetic operation on them. Multiplication and division can be written in form of addition and subtraction while operating logarithms.

There are various rules involved in performing logarithmic operations, some required for question are as follows

Product rule$\to {\mathrm{log}}_{a}m+{\mathrm{log}}_{a}n={\mathrm{log}}_{a}mn$

Exponent rule$\to {\mathrm{log}}_{a}m=y\Rightarrow m={a}^{y}$

Simplify the expression${e}^{-2x+1}=13$ by taking natural log on both sides

$\mathrm{ln}\left({e}^{-2x+1}\right)=\mathrm{ln}\left(13\right)$

$(-2x+1)\mathrm{ln}\left(e\right)=\mathrm{ln}\left(13\right),(\text{using}\text{}\mathrm{ln}\left({a}^{m}\right)=m\mathrm{ln}\left(a\right))$

$-2x+1=\mathrm{ln}\left(13\right),-\left(1\right)$

Solve equation (1) for x to get value of x

$-2x+1=2.565$

$-2x=2.565-1$

$-2x=1.565$

$x=-\frac{1.565}{2}$

$=-0.7825$

Therefore, value of x is$-0.7825$

There are various rules involved in performing logarithmic operations, some required for question are as follows

Product rule

Exponent rule

Simplify the expression

Solve equation (1) for x to get value of x

Therefore, value of x is

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