SOLUTION: Hi. I'm am required to find x in this equation: {{{log (5, (5-4x))}}} = {{{log (sqrt(5), (2-x))}}}. My teacher told me answer is +1 or -1. I do know the formula

SOLUTION: Hi. I'm am required to find x in this equation: {{{log (5, (5-4x))}}} = {{{log (sqrt(5), (2-x))}}}. My teacher told me answer is +1 or -1. I do know the formula - Change of Base La

Question 135430: Hi. I'm am required to find x in this equation: = . My teacher told me answer is +1 or -1. I do know the formula - Change of Base Law - to solve the equation, but the problem is, I do not know how to apply the formula due to the square root of 5 as the base of the equation.
I've tried by using the formula to change :
/ =
/1 =
5-4x = 2-x
-3x = -3
x = 1
However, I don't know how to find -1. Please teach me the correct method. Thanks.
(By the way, the answer is +1 with the + sign begin underlined. I hope you understand what I mean. And is this answer the same as 1 and -1? Thanks.)
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Solve for x:

Change the base of the second logarithm to that of the first using:
==
So, we end up with:
Applying the power rule to the right side:
therefore:
Simplifying:
Add 4x to both sides.
Subtract 5 from both sides.
Factor the right side.
so...
or
The answer can be read as: x = + or - 1
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