SOLUTION: If(y-1)log4 = ylog16, without using Mathematical table or calculator. Find the value of y. The bases are in 10.

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Question 1131605: If(y-1)log4 = ylog16, without using Mathematical table or calculator. Find the value of y.
The bases are in 10.
Found 3 solutions by MathLover1, Theo, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!






........log same, then

............bases same, then













Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
your equation is:

(y - 1) * log(4) = y * log(16).

y * log(16) is the same as y * log(4^2) which is the same as 2 * y * log(4).

your original equation becomes:

(y - 1) * log(4) = 2 * y * log(4)

divide both sides of this equation by log(4) and you get:

y - 1 = 2 * y

subtract y from both sides of this equation and you get:

-1 = 2 * y - y

simplify to get:

-1 = y

that's your solution.

confirm by replacing y in the original equation to get:

(y - 1) * log(4) = y * log(16) becomes (-1 - 1) * log(4) = -1 * log(16)

simplify to get -2 * log(4) = -1 * log(16).

use your calculator to get -1.204119983 = -1.204119983.

this confirms the solution is correct.

you did not use a calculator to solve this.
you only used a calculator to confirm the solution is correct.

the key to solving this is to realize that log(16) = log(4^2) and to realize that log (4^2) = 2 * log(4).

the fact that log(4^2) = 2 * log(4) is one of the properties of logs.

here's a reference on the properties of logs.

http://dl.uncw.edu/digilib/Mathematics/Algebra/mat111hb/EandL/logprop/logprop.html











Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

If(y-1)log4 = ylog16, without using Mathematical table or calculator. Find the value of y.
The bases are in 10.


 ------ Applying 

 ------ Changing 16 to base 4, or 42



Since SAME-BASE logs are equal, we get: y - 1 = 2y

                                       - 1 = 2y - y

                                        

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