Question 1131605
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.


<a href = "http://dl.uncw.edu/digilib/Mathematics/Algebra/mat111hb/EandL/logprop/logprop.html" target = "_blank">http://dl.uncw.edu/digilib/Mathematics/Algebra/mat111hb/EandL/logprop/logprop.html</a>