Question

How does this work? I don't understand

Answer 1

Explanation:

This problem is about aplying the properties of the logarithms and using aproximate values to evaluate
`log_(7)20`

There is a property of logarithms that states that the logarithm of a product will be the sum of the logarithms factor's. It means:

`Log_(x)(A*B)=log_(x)A+log_(x)B`

So, if We apply this rule to our problem, We get this:

`log_(7)20=log_(7)(2*10)`

But also

`Log_(7)(2*10)=log_(7)2+log_(7)10`

Replacing the given values in the problem, we have that:

`log_(7)(2*10)=0.356+1.183`

`log_(7)(2*10)=1.539`

`log_(7)20=1.539`

Answer 2

`\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_7(2)\approx 0.356\hspace{5em}\log_7(10)\approx 1.183 \\\\[-0.35em] ~\dotfill\\\\ \log_7(20)\implies \log_7(2\cdot 10)\implies \log_7(2)~~ + ~~\log_7(10) \\\\\\ 0.356~~ + ~~1.183 ~~ \approx ~~ 1.539`