Question

Expend log 120/49 show me the sol​

Answer 1

Hey mate, Here's the answer. . . .

$= log( \frac{120}{49} ) \\ = log(120) - log(49) \\ = log( {2}^{3} \times 3 \times 5) - log( {7}^{2} ) \\ = log( {2}^{3} ) + log(3) + log(5) - log( {7}^{2} ) \\ = 3 log(2) + log(3) + log(5) - 2 log(7)$

Hope it helps! ! !

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Regards,

Abhinay.

Answer 2

Before we solve this problem, let us know some logarithm formulae:

1. log (a * b) = log (a) + log (b)

2. log (a / b) = log (a) - log (b)

3. log (a^b) = b log (a)

Now we proceed to solve the problem.

To find: The expansion of log (120 / 49)

Solution:

Now, log (120 / 49)

We use the formula log (a / b) = log (a) - log (b):

log (120) - log (49)

= log (2^3 * 3 * 5) - log (7^2)

We use the formula log (a * b * ...) = log (a) + log (b) + ...:

log (2^3) + log (3) + log (5) - log (7^2)

We use the formula log (a^b) = b log (a):

3 log (2) + log (3) + log (5) - 2 log (7)

∴ the required expansion of log (120 / 49) is

3 log (2) + log (3) + log (5) - 2 log (7)

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