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4 years ago

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

Mathematics

1 answer:

Shkiper50 [21]4 years ago

4 0

Answer:

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

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So, if it's an inverse variation, the relationship would be

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In the second column, x = -2 and y = 7.

Now lets substitute the value of x for -2. If we get y to be 7, then the relationship is an inverse variation

We have

$\begin{gathered} y=\frac{-14}{x} \\ y=\frac{-14}{-2} \\ y=7 \end{gathered}$

Since we got y = 7, the relationship is therefore an inverse variation.

The constant k = -14

The equation for the inverse variation is

$y=\frac{-14}{x}$

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..................#2

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