SOLUTION: Find the exact value of x for which: 4^x * 5^(4x+3) = 10^(2x+3) I am aware that this question involves the change base rule, but i really need some guidance on where to start.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Find the exact value of x for which: 4^x * 5^(4x+3) = 10^(2x+3) I am aware that this question involves the change base rule, but i really need some guidance on where to start.       Log On


   



Question 304913: Find the exact value of x for which:
4^x * 5^(4x+3) = 10^(2x+3)
I am aware that this question involves the change base rule, but i really need some guidance on where to start. Your help would be much appreciated!

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
not change base, just exponents...

2^(2x) * 5^(4x) * 5^3 = 5^(2x) * 5^3 * 2^(2x) * 2^3

5^(2x) = 2^3

2x = [log(5)] / [log(8)]