SOLUTION: log 8 (sqrt 8^9) = n

Question 240807: log 8 (sqrt 8^9) = n
Found 2 solutions by jsmallt9, JimboP1977:
Answer by jsmallt9(3759) (Show Source): You can put this solution on YOUR website!

As usual, there are several ways to solve this. Maybe the quickest way is based on
knowing our exponents (including fractional exponents) well
seeing that the argument of the base 8 logarithm is a power of 8
knowing that you do not need a calculator to find the base 8 logarithm of a power of 8

Since square roots are the same as raising to the 1/2 power we can rewrite the argument:

Using the property of exponents, , we get:

Using the property of logarithms, , we can move the exponent out in front:

Since by definition :

Answer by JimboP1977(311) (Show Source): You can put this solution on YOUR website!
Log(base 8) (8^9)^(1/2) = n
Log(base 8) (8^4.5) = n
4.5 * Log(base 8) (8) = n
4.5 = n
RELATED QUESTIONS
please help me simplify these logarithms, I use {{{ log( b, N) = k }}} for logarithmic... (answered by stanbon,lwsshak3)
solve for x log(x+8)-log(x)=1 {{{ sqrt (3)^(x+1) = 9^(6x-1) }}} (answered by lwsshak3)
Given log(8) and log(9),how many of log(n) (2 <= n <= 25) can you... (answered by Edwin McCravy)
log 3/7 - log... (answered by rapaljer)
solve for x x= 6/8 (log(base6) sqrt(108) - 1 log(base6) (2/sqrt(3))+ 2 log (base6) 9 + (answered by mananth,MathTherapy,greenestamps)
Log base 8 of... (answered by josmiceli)
log(subscript 3) 8 * log(subscript 8)... (answered by stanbon,user_dude2008)
As a Single Log: log b (9) - log b... (answered by fcabanski)
{{{r^8/18}}} = m*sqrt(r^n) Then m=... (answered by ikleyn)