Im trying to solve logb(x)=3logb(2)+1/2logb(25)-logb(20)

My teacher got the following. x=2.

Not sure how to solve for x.

Thank you for the opportunity to help you with your question!

logb(x)=3logb(2)+1/2logb(25)-logb(20)

logb(x)=lobb(2^{3})+logb(25^{1/2})-logb(20)

logbb(x)=logb(8)+logb(5)-logb(20)

using the of logarithms in with addition means multiplication and minus means division then we can write the aboveequation

logb(x)=logb(8 x5÷20)

=logb(40÷20)

lobb(x)=logb(2)

thus x=2

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