Home > Precalculus > Logarithm-- Inverse of an Exponential Function

How do you change #(1/5)^4 = 1/625# into log form?

Answer 1

#4ln(5) = ln(625)#

You apply the function as such if, by "log form," you mean the natural logarithm.

#ln((1/5)^4) = ln(1/625)#

#4ln(1/5) = ln(1/625)#

#4ln(1) - 4ln(5) = ln(1) -ln(625)# technically the log of anything that is 1 is 0 #- 4ln(5) = -ln(625)# #4ln(5) = ln(625)#

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Answer 2

Xavier Alonso

To change the expression ( \left(\frac{1}{5}\right)^4 = \frac{1}{625} ) into logarithmic form, you would use the definition of logarithms. The base of the logarithm would be the base of the exponentiation, which is 1/5 in this case. The result of the exponentiation (1/625) would be the value that the logarithm evaluates to.

So, the expression in logarithmic form would be:

[ \log_{\frac{1}{5}} \left(\frac{1}{625}\right) = 4 ]

Therefore, the logarithmic form of ( \left(\frac{1}{5}\right)^4 = \frac{1}{625} ) is ( \log_{\frac{1}{5}} \left(\frac{1}{625}\right) = 4 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.