Question

ula1" title="(y - 1) log_{10}(4?) = log_{10}(16?) " alt="(y - 1) log_{10}(4?) = log_{10}(16?) " align="absmiddle" class="latex-formula">
find the value of y​

Answer 1

Answer:

3

Step-by-step explanation:

Given the log function $(y-1)log_{10}(4) = log_{10} 16$ to get the value of y, the following steps must be carried out;

$(y-1)log_{10}(4) = log_{10} 16\\\\(y-1)log_{10}(2^2) = log_{10} 2^4\\\\ (y-1)2log_{10}(2) = 4log_{10} 2\\ \\DIvide\ both\ sides\ by \ log_{10}2\\\\\frac{2(y-1)log_{10}2 }{log_{10}2} = \frac{4log_{10}2}{log_{10}2} \\\\2(y-1) = 4$

Open the bracket

$2y-2(1) = 4\\\\2y -2 = 4\\\\add \ 2 \ to \ both \ sides\\\\2y-2+2 = 4+2\\\\2y = 6\\\\Divide \ both \ sides\ by \ 2\\\\2y/2 = 6/2\\\\y = 3$

Hence the value of y is 3