Name: sandy

Question:
find X
3/2logb4-1/2logb8+logb2=logbx

my book uses prop 7 to rewrite as
logb4raised3/2-logb8raised2/3+logb2=logbx; then writes
logb8-logb4+logb2=logbx how did it get here?

Hi Sandy,

I get the second part

log_b4^3/2 = log_b8

because

4^3/2 = 2^(2)*(3/2) = 2³ = 8

and

log_b8^2/3 = log_b4

because

8^2/3 = 2^(3)*(2/3) = 2² = 4.

I don't know how you get log_b8^2/3 from 1/2log_b8 though. I hope the 1/2 was a typo that should be a 2/3.

Claude

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