SOLUTION: 3log(a)+5log(a)=64

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Question 1133622: 3log(a)+5log(a)=64
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3log%28%28a%29%29%2B5log%28%28a%29%29=64
log%28%28a%5E3%29%29%2Blog%28%28a%5E5%29%29=64
log%28%28a%5E3%2Aa%5E5%29%29=64...convert to base 10
log%28%28a%5E3%2Aa%5E5%29%29%2Flog%2810%2C%2810%29%29=64
log%28%28a%5E8%29%29=64log%2810%2C%2810%29%29
log%28%28a%5E8%29%29=log%2810%2C%2810%5E64%29%29
if log same, than
a%5E8=10%5E64
a=root%288%2C%2810%5E8%29%5E8%29
a=10%5E8


Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
3log(a)+5log(a)=64
:
use logarithm power rule
:
log(a^3) +log(a^5) = 64
:
use logarithm product rule
:
log(a^3 * a^5) = 64
:
log(a^8) = 64
:
use definition of logarithm - assume base 10
:
a^8 = 10^64
:
a = (10^64)^(1/8) = 100,000,000 = 1 * 10^8 = 1E8
: