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We can't see the parentheses, and there are at least two ways to read this.
Here are solutions for the most likely two:
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log(x) - 3 + log(x) - 2 = log(2x) + 24
Add 5 to each side:
log(x) + log(x) = log(2x) + 29
Subtract log(2x) from each side:
log(x) + log(x) - log(2x) = 29
Combine the logs on the left side, and massage:
log( x2/2x ) = log( x/2 ) = 29
Take the antilog of each side:
x/2 = 1029
Multiply each side by 2:
x = 2 x 1029
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log(x - 3) + log(x - 2) = log(2x + 24)
Combine logs on the left side:
log[ (x-3) (x-2) ] = log(2x + 24)
Take antilog of each side:
(x-3) (x-2) = 2x + 24
Expand the left side:
x2 - 5x +6 = 2x + 24
Subtract (2x+24) from each side:
x2 - 7x - 18 = 0
Factor:
(x - 9) (x + 2) = 0
Whence:
x = 9
x = -2
We have to discard the solution [ x = -2 ] because one term in the equation
is log(x-2).
If 'x' were -2 then we'd have log(-4) but negative numbers don't have logs.
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