Question

Choose the single logarithmic expression that is equivalent to the one shown 5 log x + 3 log x^2

Answer 1

Hey


`5 log(x) + 3 log( {x}^(2) )`


`= log( {x}^(5) ) + log( {x}^(6) )`


`= log( {x}^(5) * {x }^(6) )`


`= 11 log(x)`

Answer 2

`5 log x + 3 log x^(2) = 11 log x`

Explanation:

Given the logarithmic expression

`5 logx + 3 log x^2`

Logarithm rule: when we take log with any number raise to power x

Then the power x move down before the log and write log with the base of number

For example : Let we take a number
`2^x`

When we take log then power x go down and write before the log and take log with the given base of that number

Therefore we can write as x log 2

Now , we have logarithmic expression

`5logx + 3 log x^2`

=
`5 logx + 6 log x`

=
`11 logx`

Hence, the logarithmic expression
`5 log x + 3 log x^2` is equivalent to
`11 log x`.