Question #c615c

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Answer 1 · 2018-01-30T00:04:57

Given: #3^(2x+1)=5#

Use the natural logarithm on both sides:

#ln(3^(2x+1))=ln(5)#

An important property of logarithms is that it allows one to move the exponent outside of the argument as a factor:

#(2x+1)ln(3)=ln(5)#

Divide both sides by #ln(3)#:

#2x+1=ln(5)/ln(3)#

Subtract 1 from both sides:

#2x=ln(5)/ln(3)-1#

Divide both sides by 2:

#x=(ln(5)/ln(3)-1)/2#

Use a calculator:

#x = 0.232487#