Question

if log12)27=a then log(6)64= ​

Answer 1

Answer:

4(3+a/3-a)

Step-by-step explanation:

you are writing aiats

Answer 2

Answer:

The value of the logarithm is

$log_{6}(64) = \frac{6(3 - a)}{3 + a}$

Step-by-step explanation:

Given logarithm is

$log_{12}(27) = a$

We have an formula for logarithms which is

$log_{b}(a) = \frac{log \: a}{log \: b}$

Therefore given logarithm becomes

$\frac{log \: 27}{log \: 12} = a \\ = > \frac{log(3) {}^{3} }{log(3 \times 4)} = a \\ = > \frac{3log3}{log3 + log4} = a \\ = > 3log3 = alog3 + 2alog2 \\ = > log3 = \frac{2alog2}{ 3 - a}$

Now the given logarithm is

$log_{6}(64)$

We can rewrite it as

$\frac{log64}{log6} = \frac{log2 {}^{6} }{log(2 \times 3)} \\ = \frac{6log2}{log2 + log3}$

Substituting value of log3 in above equation,we get

$= > \frac{6log2}{log2 + \frac{2alog2}{3 - a} } \\ = \frac{6}{3 +a } \times (3 - a) \\ = \frac{6(3 - a)}{3 + a}$

Therefore,the value of given logarithm is

$log_{6}(64) = \frac{6(3 - a)}{3 + a}$

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