Question 1131605

If(y-1)log4 = ylog16, without using Mathematical table or calculator. Find the value of y.
The bases are in 10.
<pre>{{{matrix(1,3, (y - 1) * log ((4)), "=", y * log(16))}}}
{{{matrix(1,3, log ((4))^(y - 1), "=", log ((16))^y)}}} ------ Applying {{{matrix(1,3, a * log((b)), "=", log ((b))^a)}}}
{{{matrix(1,3, log ((4))^(y - 1), "=", log ((4^2))^y)}}} ------ Changing 16 to base 4, or 4<sup>2</sup>
{{{matrix(1,3, log ((4)^(y - 1)), "=", log ((4))^(2y))}}}
Since SAME-BASE logs are equal, we get: y - 1 = 2y
                                       - 1 = 2y - y
                                       {{{highlight_green(matrix(1,3, - 1, "=", y))}}}