Question

Rewrite this using properties of logarithms

Answer 1

D.
`\log_4(3\sqrt[3]{35})`

Explanation:

The given logarithmic expression is:

`\log_43+(\log_45)/(3) +(\log_47)/(3)`

Don't let the fractions scare you at all.

We can rewrite the expression in another form that makes the fractions a bit friendly.

Recall that:
`\boxed{(x)/(3)=(1)/(3)x}`

We apply this knowledge to get:

`\log_43+(1)/(3)\log_45 +(1)/(3)\log_47`

We can now use the following property:

`n \log_am=\log_am^n`

We apply this property to get:

`\log_43+\log_45^{(1)/(3)} +(1)/(3)\log_47^{(1)/(3)}`

Recall again that:

`\log_am+\log_an+\log_ap=\log_amnp`

`\log_43* 5^{(1)/(3)} *7^{(1)/(3)}`

`\log_43* (5*7)^{(1)/(3)}`

`\log_43* (35)^{(1)/(3)}`

`\log_43\sqrt[3]{35}`

The correct choice is D.