Question

expand log 120/
49......​

Answer 1

expansion of log120/49 is given below

Step-by-step explanation:

prime factorisation of 120= 2 ×2×2×3×5=2³ ×3×5

     Prime Factorisation of 49 = 7×7=  7²

log  120/49= log120 -log49    as loga/b= log a-log b

                     =log 2³ ×3×5  - log  7²

                       = log 2³ + log 3+ log5 - log  7²  as( log a×b= loga +log b)

                        =3log 2 +log3 + log 5 - 2log7  as( log a² = 2loga)

Answer 2

The expandatation of $\log \dfrac{120}{49}$ $=3\log 2+\log3 + \log 5-2\log7$  

Step-by-step explanation:

We have,

$\log \dfrac{120}{49}$

To expand $\log \dfrac{120}{49}$ = ?

∴ $\log \dfrac{120}{49}$

Using the logarithm identity,

$\log \dfrac{a}{b}=\log a-\log b$

$=\log (2^3\times 3\times 5)-\log 7^2$

Using the logarithm identity,

$\log ab=\log a+\log b$ and

$\log a^n=n\log a$

$=\log 2^2+\log 3+\log 5 -\log 7^2$

$=3\log 2+\log3 + \log 5-2\log7$

Thus, the expandatation of $\log \dfrac{120}{49}$ $=3\log 2+\log3 + \log 5-2\log7$