SOLUTION: given log(base a)x=4, log(base a)y=3, and log(base a)z=2 for constants x, y,z. find the value of the logarithm. log(base a)((5th root of y^3 times x^6 times z^4)/(5th root of z^

Question 244998: given log(base a)x=4, log(base a)y=3, and log(base a)z=2 for constants x, y,z. find the value of the logarithm.
log(base a)((5th root of y^3 times x^6 times z^4)/(5th root of z^6 times x^2)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you are given:

log(a,x) = 4
log(a,y) = 3
log(a,z) = 2

you want to find:

since , your equation becomes:

since log(a^b) = b*(log(a), your equation becomes:

since log(a/b) = log(a)/log(b), your equation becomes:

since log(a*b) = log(a) + log(b), your equation becomes:

since log(a^b) = b*log(a), your equation becomes:

from here on it's just a straight substitution since you are given:

log(a,x) = 4
log(a,y) = 3
log(a,z) = 2

your equation of:

becomes:

which becomes:

which becomes:

which becomes:

RELATED QUESTIONS
Knowing that x = log(base a)2 , y = log(base a)3, z=log(base a)5 express the following... (answered by lwsshak3)

Use the following information to help you answer (a), (b), and (c). log(base d) X = 4 (answered by stanbon)

Let log base a x= -5, log base a y =2 and log base a z=0.25. determine the values of the... (answered by MathLover1)

The sides of a triangle have lengths log(base 2)3, log( base 2)7,and log(base 2) x. Find... (answered by KMST)

Please help me solve this eqaution: Express as a single logarithm and, if possible,... (answered by ankor@dixie-net.com)

how to express as a logarithm of a single number: 1. 7 log base2 x- 1/3 log base2 y (answered by stanbon)

log base a of sqrt (a*x^12/y^2) given log base a of x=-8.2 and log base a of y=4... (answered by lwsshak3)

Rewrite each of the following as sums and differences of a logarithm of some number. a.... (answered by LinnW)

log base x (w)=24, log base y (w)=40, log base xyz (w)=12. Find log base x (y) log... (answered by ikleyn)