Before solving the equation, we'll create matching bases.
We'll switch between the bases and numbers of both logarithms, using the
formula:
log a b = 1/log b
a
log x 2 = 1/ log 2 x
log
sqrtx 2 = 1/log 2 sqrtx
But log 2 sqrt x = log 2
x^1/2
We'll apply the power property to the number log 2
x^1/2.
log 2 x^1/2 = (log 2
x)/2
We'll re-write the
equation:
1/log 2 x + 2/log 2 x =
9
We'll substitute log 2 x =
t
We'll re-write the equation in
t:
1/t + 2/t =
9
1+2=9t
9t =
3
t = 3/9
t =
1/3
log 2 x =
1/3
x =
2^(1/3)
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