Question

expand log(1125/32)​

Answer 1

Answer:

LOG 1125-LOG 32

Step-by-step explanation:

LOG 1125-LOG 32 =LOG(1125/32)

Answer 2

The expansion of log (1125/32) is equal to 3log(5) + 2log(3) - 5log(2).

Given:

The given expression is log (1125/32).

To Find:

The expansion of log (1125/32).

Solution:

→ The basic properties of logarithms are:

(i) log (mn) = log (m) + log (n)

(ii) log (m/n) = log (m) - log (n)

(iii) log (m)ⁿ = n log (m)

→ We would now use the above properties to expand the log (1125/32):

                                  $\boldsymbol{= log(\frac{1125}{32} ) }\\\\\boldsymbol{= log(1125)-log(32)}\\\\\boldsymbol{=log(125\times9)-log(2^{5})}\\\\\boldsymbol{ =log(125)+log(9)-5log(2)}\\\\\boldsymbol{=log(5^{3} )+log(3^{2} )-5log(2)}\\\\\boldsymbol{=3log(5)+2log(3)-5log(2)}$

∴ The expansion of log (1125/32) is equal to 3log(5) + 2log(3) - 5log(2).

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