SOLUTION: log base 4 of 5 + log base 4 of x = log 4 of 60

Question 722248: log base 4 of 5 + log base 4 of x = log 4 of 60
Found 2 solutions by stanbon, DrBeeee:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
log base 4 of 5 + log base 4 of x = log 4 of 60
-------
log4(5) + log4(x) = log4(60)
----
log4(5x) = log4(60)
------
5x = 60
x = 12
-------------
Cheers,
Stan H.
=============
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
I assume the right side is log base 4 of 60. I'll use L4 to represent log base 4. In this problem it doesn't matter what base of the log is, just that they are all the same.
The left side is the sum of the logs of two numbers which is the same as the log of the product of the two numbers. So we have
(1) L4(5*x) = L4(60)
Take the inverse log of each side of (1) and we get
(2) 5*x = 60 or
(3) x = 12
Let's check this.
Is (L4(5) + L4(12) = L4(60))?
Is (L10(5)/L10(4) + L10(12)/L10(4) = L10(60)/L10(4))?
Is (L10(5) + L10(12) = L10(60))?
Is (0.69897.. + 1.079... = 1.778...)?
Is (1.778,,, = 1.778...)? Yes
Answer: x equals 12.
RELATED QUESTIONS
how do you solve log base 4 (log base 3 (log base 2 of X)) = 0?? (answered by stanbon)
log base 4 of... (answered by ikleyn,josgarithmetic,MathTherapy)
Expand log Log base 4 of... (answered by MathLover1)
Log base 8 of 16+ log base 8 of... (answered by nerdybill)
Log base 0.4 of 24 - log base 4 of... (answered by nerdybill)
find x log base 2 (log base 3 (log 4 of... (answered by greenestamps)
solve for x: log 2 (log 3 x) = 4 -----> log of (log of x base 3) base 2 equals 4 (answered by jsmallt9)
Write in terms of the NATURAL LOG. (ln) 1. log (base 4)x 2. log (base 10) (x+1) 3. log (answered by solver91311,jsmallt9)
Find all real values of x such that log base 2 of (log base 2 of x)= log base 4 of (log... (answered by Theo)