SOLUTION: Solve: log base 4 (X) + Log base 8 (x) = 1 ln X/ln 4 + ln X/ln 8=1 2 ln X/2 ln 4 + ln X/ln 8 = 2 ln X^2 + ln X = 2 ln 8 ln X^2 + ln X - 2 ln 8 = 0 ln X^2(x)-2 ln 8 = 0 ln X

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve: log base 4 (X) + Log base 8 (x) = 1 ln X/ln 4 + ln X/ln 8=1 2 ln X/2 ln 4 + ln X/ln 8 = 2 ln X^2 + ln X = 2 ln 8 ln X^2 + ln X - 2 ln 8 = 0 ln X^2(x)-2 ln 8 = 0 ln X      Log On


   

Question 372029: Solve:
log base 4 (X) + Log base 8 (x) = 1
ln X/ln 4 + ln X/ln 8=1
2 ln X/2 ln 4 + ln X/ln 8 = 2
ln X^2 + ln X = 2 ln 8
ln X^2 + ln X - 2 ln 8 = 0
ln X^2(x)-2 ln 8 = 0
ln X^3 - 2 ln 8 = 0
ln X^3 / 2 ln 8 = 0
ln X^3/ln 64
I am not sure this is done right?????
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2C%28X%29%29%2Blog%288%2C%28X%29%29=1
y1%2By2=1
By definition,
y1=log%284%2C%28X%29%29
X=4%5E%28y1%29
X=%282%5E2%29%5Ey1
X=2%5E%282%2Ay1%29
.
.
y2=log%288%2C%28X%29%29
X=8%5E%28y2%29
X=%282%5E3%29%5Ey2
X=2%5E%283%2Ay2%29
.
.
They both equal X so set them equal to each other.
2%5E%282%2Ay1%29=2%5E%283%2Ay2%29
2%2Ay1=3%2Ay2
y1=%283%2F2%29y2
Substituting,
y1%2By2=1
%283%2F2%29y2%2By2=1
%285%2F2%29y2=1
y2=2%2F5
log%288%2C%28X%29=2%2F5%29
highlight%28X=8%5E%282%2F5%29%29