SOLUTION: Hi, this is my second time asking a question....both were on logarithms :( Solve for x. {{{ log( 2, x+1 ) }}} = {{{ log( 4, x+3 ) }}} Because {{{ log( 4, x+3 ) }}} can be re

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Question 891981: Hi, this is my second time asking a question....both were on logarithms :(
Solve for x.
=
Because can be rewritten as ,
it was = . Then,
=
Thus,
But I don't know what to do next. Or did I do wrong from the beginning?
I know there could be another way... for example... making = to make the same base for both sides. But still, I don't know what to do next.
Could you please teach me how to solve this problem in those two ways?
Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Solve for x.
=
-------------
can be rewritten as
--------------
=
=


(x-1)*(x+2) = 0
x = 1
=============
x = -2 is rejected, gives log of a neg value
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Hi, this is my second time asking a question....both were on logarithms :(
Solve for x.
=
Because can be rewritten as ,
it was = . Then,
=
Thus,
But I don't know what to do next. Or did I do wrong from the beginning?
I know there could be another way... for example... making = to make the same base for both sides. But still, I don't know what to do next.
Could you please teach me how to solve this problem in those two ways?




 ------ Applying change of base

 ----- Changing base on right to base 2



 ------- Cross-multiplying











(x - 1)(x + 2) = 0

	   	      OR	         x = - 2 (ignore)



After you'd obtained,  = , you should have had: , which is

the same as: 

 ------- Squaring both sides

Go on to solve for x. 

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