Question

Evaluate the Logarithim log6 1/36 base 6 I need steps please.

Answer 1

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Rewrite as an equation.log6(136)=xRewrite log6(136)=x in exponential form using the definition of a logarithm. If x and b are positive real numbers and b does not equal 1, then logb(x)=y is equivalent to by=x.6x=136Create equivalent expressions in the equation that all have equal bases.6x=6−2Since the bases are the same, the two expressions are only equal if the exponents are also equal.x=−2The variable x is equal to −2.−2

Answer 2

Answer:

$\log _6\left(\frac{1}{36}\right)=-2$

Step-by-step explanation:

Consider the given expression $\log _6\left(\frac{1}{36}\right)$

We have to find the value of given expression $\log _6\left(\frac{1}{36}\right)$

Consider the given expression $\log _6\left(\frac{1}{36}\right)$

$\mathrm{Apply\:log\:rule}:\quad \log _a\left(\frac{1}{x}\right)=-\log _a\left(x\right)$

We have,

$=-\log _6\left(36\right)$

$\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)$

$\log _6\left(6^2\right)=2\log _6\left(6\right)$

We have,

$=-2\log _6\left(6\right)$

$\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1$

$\log _6\left(6\right)=1$

Thus, $\log _6\left(\frac{1}{36}\right)=-2$