Question

hello i just wanted to check my answer in this test in math :]] i'm not sure if i did everything correctly

Answer 1

`\log _3(\frac{3^{(2)/(3)}}{2^{(1)/(3)}})+\log _(27)(6)\approx1`

1) Let's simplify this logarithm expression, making use of properties.

`(2)/(3)\log _36-(1)/(3)\log _38+\log _(27)6`

2) Let's rewrite that expression turning the factor 2/3 back into an exponent

as well as that -1/3:

`\begin{gathered} \log _3\mleft(6^{(2)/(3)}\mright)-\log _3\mleft(8^{(1)/(3)}\mright)+\log _(27)\mleft(6\mright) \\ \end{gathered}`

Now, let's rewrite that difference into a quotient:

`\begin{gathered} \log _3\mleft(\frac{3^{(2)/(3)}}{2^{(1)/(3)}}\mright)+\log _(27)\mleft(6\mright) \\ 0.4563+0.5436\approx1 \end{gathered}`

Since the question does not allow the use of calculator, then we can leave it as the simplest possible expression. Although, the answer is approximately 1.