(y - 1) log_(10)(4?) = log_(10)(16?) find the value of y​

Question

`(y - 1) log_(10)(4?) = log_(10)(16?)`
find the value of y​

Answer 1

3

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\\\\(2(y-1)log_(10)2 )/(log_(10)2) = (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