SOLUTION: How do I solve- If 2^a=3^b=6^c, show that c=ab/a+b. Thank you

Algebra.Com
Question 979068: How do I solve-
If 2^a=3^b=6^c, show that c=ab/a+b.
Thank you

Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
2^a=6^c ---> (2^a)^(b/a+b)=(6^c)^(b/a+b) ---> 2^(ab/(a+b))=6^(cb/(a+b))
3^b=6^c ---> (3^b)^(a/a+b)=(6^c)^(a/a+b) ---> 3^(ab/(a+b))=6^(ca/(a+b))
Then, multiplying
[ 2^(ab/(a+b)) ] [ 3^(ab/(a+b)) ] = [ 6^(cb/(a+b)) ] [ 6^(ca/(a+b)) ]
(2*3)^(ab/(a+b)) = 6^[ cb/(a+b) + ca/(a+b) ]
6^(ab/(a+b)) = 6^[(cb+ca)/(a+b)]
6^(ab/(a+b)) = 6^[c(b+a)/(a+b)]
6^(ab/(a+b)) = 6^c ------> ab/(a+b) = c

RELATED QUESTIONS

Find a^2+b^2+c^2 If a+b=c+6 and ab-ac=bc-1 please help me to solve this kind of math... (answered by jim_thompson5910,josgarithmetic)
If A(-1,-7) B(2,2) C(4,8), show that C lies on AB. So I found that the general... (answered by josgarithmetic)
Please solve: (x^2-ax+b)is a factor of x^3+3ax^2+3bx+c Show that b=-2a^2 (answered by CharlesG2)
Please, i need your help to understand how to solve the measurement of the hypotenuse. I... (answered by jim_thompson5910)
how do i solve... directions: write a quadratic equation with the given roots. Write the (answered by Alan3354,richard1234)
please help me with this problem & show work so that I know how to do the other problems. (answered by Cromlix)
if a =1, b =2, c= -3 find the value of c-ab c+ab (answered by elima)
Need help on these that I have to complete today Evaluate for a=3 and b= -4 1.a.... (answered by Earlsdon,Mathtut)
I need help in solving the below equation. I do not understand how the answer is 4y.... (answered by ewatrrr)