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Andrew [12]
3 years ago
5

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

Mathematics
2 answers:
Dimas [21]3 years ago
8 0
L
Rewrite as an equation.<span><span>log6</span><span>(<span>136</span>)</span>=x</span>Rewrite <span><span>log6</span><span>(<span>136</span>)</span>=x</span> in exponential form using the definition of a logarithm. If x and b are positive real numbers and b does not equal 1, then <span><span>logb</span><span>(x)</span>=y</span> is equivalent to <span><span>by</span>=x</span>.<span><span>6x</span>=<span>136</span></span>Create equivalent expressions in the equation that all have equal bases.<span><span>6x</span>=<span>6<span>−2</span></span></span>Since the bases are the same, the two expressions are only equal if the exponents are also equal.<span>x=−2</span>The variable x is equal to <span>−2</span>.<span>−<span>2</span></span>
joja [24]3 years ago
7 0

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

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