Most impotently the logarithm function is an injection (one-to-one) function.I would like to understand algebraically what happens for an equation with both logs with the same base to become A = B. Example:
log (2x + 1) = log 11
2x + 1 = 11
Especially, why both sides have to have the same base?
Actually, it's the exact opposite of "impotent" -- it's "important"! (This is why I proofread.)Most impotently the logarithm function is an injection (one-to-one) function.
Thus if \(\log_b(X)=\log_b(Y)\text{ then }X=Y\) .
The same reason as in:Hello,
I would like to understand algebraically what happens for an equation with both logs with the same base to become A = B. Example:
log (2x + 1) = log 11
2x + 1 = 11
Thank you in advance!
But posts that are NOT proof read are often more fun to read!Actually, it's the exact opposite of "impotent" -- it's "important"! (This is why I proofread.)
To put it another way, you can exponentiate both sides (raise b to each power), which eliminates the logs because the log is the inverse function of the exponential. If two numbers have the same log, then they must be the same number, because both are the same power of the base.