Expert: Sherman D. - 12/24/2004

Question
If log(x+1)  64=2, find x. (The (x+1) is small  and is the base of the log.)
I used the change of base formula, thus doing (log 64)/(log(x+1))=2; however, then, I didn't know how to finish the example and find x. Please show me how using my method as I know a different method that will work already and will get x=7. Thank you.


Answer
Hey Jeff, my best customer, lol.

there is a better method for doing this

log(x + 1)64 = 2

log(base a)x = y
becomes
a^y = x

so

log(x + 1)64 = 2
becomes
(x + 1)^2 = 64

sqrt both sides and you get

x + 1 = ±8

subtract 1 from both sides

x = 7 or -9

now since you can't have a negative base, the answer is

x = 7

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If you were to do it your way

(log 64)/(log(x + 1)) = 2

becomes

(log 64)/2 = log(x + 1)

once you work (log 64)/2, then inverse log both sides, you get

x + 1 = 8

subtract both sides and you get

x = 7