Question

The Value of

$( \frac{1}{ log _312} + ( \frac{1}{ log_{4}12 } )$
is Equal' to​

Answer 1

Answer:

1

Step-by-step explanation:

$\frac{1}{ log_{3}(12) } + \frac{1}{ log_{4}(12) }$

Before We go further Some laws of Logarithm.

$log_{b}(a) = \frac{1}{ log_{a}(b) }$

$log_{m}{a \times b} = log_{m}(a) + log_{m}(b)$

$log_{a}(a) = 1$

So,We can Write

1/log_3^12=log_12^3

1/log_4^12=log_12^4

$log_{12}(4) + log_{12}(3)$

Now it is in form of

log_m(a)+log_m(B)

It can be written as

$log_{12}(3 \times 4) \\ \\ log_{12}(12) \\ \\ = 1$

Answer=1

Answer 2

Answer : 1

Explanation :-

1/log_3(12) + 1/log_4(12)

1/log_3^12 = log_12^3

1/log_4^12 = log_12^4

log_12(4) + log12(3)

So,

log_n(a) + log_m(B)

» log_12(12)

= 1

Answer = 1