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# How to deal with (logbased3 of x)^2?

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The Q is

(logbased3 of x)^2 - 3logbased3 of x = 10

Solve for x. How should I deal with this parenthesis x? Should i use the U substitution? Thanks in advanced.

Nov 7, 2018

### Best Answer

#1
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First, let y = log3(x).  Then:

y2 - 3y - 10 = 0

This factors as:  (y - 5)(y + 2) = 0

So y = 5 and y = -2 are solutions for y.

So, we have 5 = log3(x), which means x = 35

Also -2 = log3(x), which means x = 3-2

Nov 7, 2018

### 2+0 Answers

#1
+3
Best Answer

First, let y = log3(x).  Then:

y2 - 3y - 10 = 0

This factors as:  (y - 5)(y + 2) = 0

So y = 5 and y = -2 are solutions for y.

So, we have 5 = log3(x), which means x = 35

Also -2 = log3(x), which means x = 3-2

Alan Nov 7, 2018
#2
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THANKS! That cleara it up! Just basic algebraic manipulation.

Guest Nov 7, 2018