I need help on solving for x in this log


label Algebra
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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.

Oct 1st, 2015

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

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

logb(x)=lobb(23)+logb(251/2)-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


Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 1st, 2015

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