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# Logarithmic equation to Exponential form and vice versa

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I missed a day of math class last week and was wondering if someone could break it down to me how to change a logarithmic equation into exponential form and vice versa. I provided an examples from my makeup work below.

*Write the logarithmic equation in exponential form.
1. ln sqrt e = (1/2)

*Write the exponential equation in Logarithmic form
1. e^1.3 = 3.6692

Sep 4, 2017

#1
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$$ln(\sqrt e)=\frac{1}{2}$$

ln is just log base "e".

$$log_{e}(\sqrt e)=\frac{1}{2}$$

To convert this expression to an exponent, we take the log base, put it to the power of the otherside of the equation, and then put that equal to what was in the logs brackets.

$$e^{\frac{1}{2}}=\sqrt{e}$$

.
Sep 4, 2017

#1
+1

$$ln(\sqrt e)=\frac{1}{2}$$

ln is just log base "e".

$$log_{e}(\sqrt e)=\frac{1}{2}$$

To convert this expression to an exponent, we take the log base, put it to the power of the otherside of the equation, and then put that equal to what was in the logs brackets.

$$e^{\frac{1}{2}}=\sqrt{e}$$

Will85237 Sep 4, 2017