Sure! Let's evaluate the given expressions step by step.
### 1) [tex]\(\log_3(27)\)[/tex]
To solve for [tex]\(\log_3(27)\)[/tex], we need to find the exponent [tex]\(x\)[/tex] such that:
[tex]\[ 3^x = 27 \][/tex]
Observing that 27 can be rewritten as a power of 3:
[tex]\[ 27 = 3^3 \][/tex]
Thus:
[tex]\[ 3^x = 3^3 \][/tex]
Since the bases are the same, the exponents must be equal:
[tex]\[ x = 3 \][/tex]
Therefore:
[tex]\[ \log_3(27) = 3 \][/tex]
### 2) [tex]\(\log_6\left(\frac{1}{36}\right)\)[/tex]
To solve for [tex]\(\log_6\left(\frac{1}{36}\right)\)[/tex], we need to find the exponent [tex]\(y\)[/tex] such that:
[tex]\[ 6^y = \frac{1}{36} \][/tex]
First, we observe that [tex]\(\frac{1}{36}\)[/tex] can be expressed as a power of 6:
[tex]\[ \frac{1}{36} = 6^{-2} \][/tex]
Thus:
[tex]\[ 6^y = 6^{-2} \][/tex]
Since the bases are the same, the exponents must be equal:
[tex]\[ y = -2 \][/tex]
Therefore:
[tex]\[ \log_6\left(\frac{1}{36}\right) = -2 \][/tex]
So, the evaluated results for the given logarithmic expressions are:
[tex]\[ \boxed{3 \text{ and } -2} \][/tex]
