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log(1/6)36 what is the answer its not 6???

Sagot :

vhv1122
turn it into exponent form, so Log(1/6)36 ⇒ (1/6)^x=36
1. 6²=36
2. (1/6)²=(1²/6²)=1/36
so Log(1/6)36=2
:) hope that helped...

Answer:

[tex]\text{log}_{\frac{1}{6}}(36)=-2[/tex]

Step-by-step explanation:

We have been given a logarithm expression [tex]\text{log}_{\frac{1}{6}}(36)[/tex]. We are asked to evaluate our given expression.

Using logarithm rule [tex]log_{\frac{1}{a}}(x)=-log_a(x)[/tex], we can write our expression as:

[tex]\text{log}_{\frac{1}{6}}(36)=-\text{log}_6(36)[/tex]

[tex]\text{log}_{\frac{1}{6}}(36)=-\text{log}_6(6^2)[/tex]

Using logarithm rule [tex]\text{log}_{a}(x^b)=b\text{log}_a(x)[/tex], we will get:

[tex]\text{log}_{\frac{1}{6}}(36)=-2\text{log}_6(6)[/tex]

Applying rule [tex]\text{log}_{a}(a)=1[/tex], we will get:

[tex]\text{log}_{\frac{1}{6}}(36)=-2\cdot 1[/tex]

[tex]\text{log}_{\frac{1}{6}}(36)=-2[/tex]

Therefore, [tex]\text{log}_{\frac{1}{6}}(36)=-2[/tex].

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