Question

what is the answer


please answer with step by step explanation.

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Answer 1

Topic :-

Logarithm

Question :-

$\sf{The\:value\:of\:\log_{343}49.}$

Solution :-

$\sf {\mapsto \log_{343}49}$

$\sf {\mapsto \log_{343}7^2}$

$\sf{(\because 49=7^2)}$

$\sf {\mapsto 2\log_{343}7}$

$\sf {(\because \log_{a}m^n=n\log_a m)}$

$\sf {\mapsto 2\log_{7^3}7}$

$\sf{(\because 343=7^3)}$

$\sf {\mapsto \dfrac{2}{3}\log_{7}7}$

$\sf {\left(\because \log_{m^n}a=\dfrac{1}{n}\log_ma\right)}$

$\sf {\mapsto \dfrac{2}{3}\times 1}$

$\sf {\left(\because \log_{a}a=1\right)}$

$\sf {\mapsto \dfrac{2}{3}}$

Answer :-

$\underline{\boxed{\sf{\log_{343}49=\dfrac{2}{3}}}}$

Hence, option B is correct option.

Additional Formulae :-

$\sf{\log mn=\log m + \log n}$

$\sf{\log \left(\dfrac{m}{n}\right)=\log m - \log n}$

$\sf{\log 1=0}$

$\sf{\log_a\left(\dfrac{1}{a}\right)=-1}$

$\sf{\log_{\tfrac{1}{a}}a=-1}$

$\sf{\log_am=\dfrac{1}{\log_ma}}$

$\sf{a^{\log_am}=m}$

$\sf{\log_ax=\dfrac{\log x}{\log a}}$

Answer 2

Answer:

The Great Himalayan range is also called Himadri. The world's highest peak, Mount Everest, and other highest peaks like K2, Nanga Parbat, Kangchenjunga etc are part of the Greater Himalayan range

Step-by-step explanation:

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