#5^(3n)=125# how do you solve this exponential equation?

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Answer 1 · 2018-04-12T17:14:27

#n = 1#

Given: #5^(3n)=125#

Use the natural logarithm on both sides:

#ln(5^(3n))=ln(125)#

Use the property of logarithms, #ln(a^c)= (c)ln(a)#:

#(3n)ln(5)=ln(125)#

Multiply both sides by #1/ln(5)#:

#3n=ln(125)/ln(5)#

Multiply both sides by #1/3#:

#n=1/3ln(125)/ln(5)#

Use a calculator:

#n = 1#