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How do you solve for x with different log bases?
log(base 4)(x + 6) = log(base 2)(x)
1 Answer
- 1 decade agoFavorite Answer
You can always turn all the logarithms into the same base by the change of base formula:
log(base b)a = log(base c)a/log(base c) b = log a/log b = ln a/ln b
In this case, instead of the change of base formula, you could do this:
4^(log(base 4)(x+6)) = 4^(log(base 2)x)
x + 6 = 2^(2* log(base 2)x = 2^log(base 2)x^2 = x^2
x = 3, -2
but -2 doesn't work so the answer is 3
