Question

Log 7 base 105 equal to a log 5 base 7 equal to b then log 105 base 35 is equal to

Answer 1

Answer:

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Answer 2

Answer:

Required value is $\frac{b + 1}{ab}$

Step-by-step explanation:

Given,

$log_{7}(105) = a.....(1)$and $log_{5}(7) = b......(2)$

Here we want to find value of$log_{105}(35)$

We can write,

$log_{105}(35) = log_{105}(5 \times 7) = log_{105}(5) + log_{105}(7)$

Here,$log_{7}(105) = a$

So,

$\frac{1}{ log_{105}(7) } = a \\ log_{105}(7) = \frac{1}{a} .......(3)$

From equation (2) and (3)

$log_{5}(7) \times log_{7}(105) = a\times b$

So,$ab = log_{5}(105)$

So,$\frac{1}{ log_{105}(5) } = ab \\ log_{105}(5) = \frac{1}{ab}$

Now,$log_{105}(5) + log_{105}(7) = \frac{1}{a} + \frac{1}{ab} = \frac{b + 1}{ab}$

Required value is $\frac{b + 1}{ab}$

Here applied formula,

$1.log_{x}(y) \times log_{z}(x) = log_{z}(y) \\ 2. log_{x}(y) = \frac{1}{ log_{y}(x) } \\ 3. log_{x}(y) + log_{x}(z) = log_{x}(yz)$