Expert: Bobby Soltani - 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
Hi Jeff,

Here are the steps from where you left off:

(log 64)/(log(x+1) = 2
log 64 = log(2^6) = 6*log(2)
6*log(2)/log(x+1) = 2
multiply both sides by log(x+1)
6*log(2) = 2*log(x+1)
divide both sides by 2
3*log(2) = log(x+1)
move the three up to become 2^3 (this is a property of logarithms.  For example 7log(3) = log(3^7).

log(2^3) = log(x+1)
2^3 = 8
log(8) = log(x+1)
take both sides to the power of 10
10^log(8) = 10^(log(x+1))
the log disappears.  Another property of logs.  10^log(x) = x
8 = x + 1
subtract 1 from both sides
x = 7

I hope this helps you out.  Let me know if you have any questions.  Happy Holidays.

Bobby