SOLUTION: log (base 5) x + log (base 3) x = 1 the answer is 1.921, but i want to know how they got it.

Question 516128: log (base 5) x + log (base 3) x = 1
the answer is 1.921, but i want to know how they got it.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
log (base 5) x + log (base 3) x = 1
===================
log(x)/log(5) + log(x)/log(3) = 1
----
Multiply thru by log(5)*log(3) to get:
log(3)*log(x) + log(5)log(x) = log(5)*log(3)
log(x)[log(3)+log(5)] = log(5)*log(3)
log(x)*log(15) = log(5)*log(3)
---
log(x) = [log(5)*log(3)]/log(15)
---
log(x) = 0.2836
---
x = 10^0.2836
---
x = 1.9211
===============
Cheers,
Stan H.
=======================
RELATED QUESTIONS
log(base 16) x + log(base 4 x + log(base 2) x = 7 the answer is 16, but i want to know... (answered by scott8148)

Can you help me solve this log for x? log base 2 of(x+1) - log base 2 of x= log base 2... (answered by ewatrrr)

How do I solve log 5 to the base negative 1 over 125 minus log 4 to the base 64 plus log... (answered by stanbon)

log base 3 (x) = log base 3 (1/x)+4 i understand that log base 3 (1/x) is subtracted... (answered by solver91311)

Please assist with the steps to solve this equation. I know the answer, but want to see... (answered by lwsshak3)

I know the answer is 2 but i dont know how to get it can you please help me? log(base... (answered by jsmallt9)

I'm trying to convert this equation: log base 100 (1/100x). I got to Log base 100 (1) -... (answered by jsmallt9)

please help me solve log base 6 X + log base 6 X-3=2 the answer is 7.365 but I need... (answered by lwsshak3)

log(base 4) (x+13) - log(base 4)(x-8) = 1 I know the answer is 15 but why in the... (answered by ewatrrr)