Question

If log8 base 10 =x and log3base10 =y express log720 base 10 in teems of x and y

Answer 1

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❚ QuEstiOn ❚

If ,

$\longrightarrow \log_{10}8=x$

$\longrightarrow \log_{10}3=y$

Then , express , $\log_{10}720$ in terms of x and y ,

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❚ ANsWeR ❚

✺ Given :

• $\longrightarrow \log_{10}8=x$
• $\longrightarrow \log_{10}3=y$

✺ To Express :

• $\log_{10}720$ in terms of x and y ,

✺ Explanation :

$\longrightarrow \log_{10}720$

$\longrightarrow \log_{10}(8\times9\times10)$

$\longrightarrow \log_{10}8+\log_{10}9+\log_{10}10$

$\longrightarrow \log_{10}8+\log_{10}3^2+\log_{10}10$

$\longrightarrow \log_{10}8+2\log_{10}3+\log_{10}10$

❮ putting the value , of $\log_{10}8=x$ & $\log_{10}3=y$ ❯

$\longrightarrow (x+2y+1)$ (answer)

✺ Therefore :

$\log_{10}720$ = (x+2y+1)

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❏ Formula Used :-

$\longrightarrow \log_{e}(a\times b\times c)=\log_{e}a+\log_{e}b+\log_{e}c$

$\longrightarrow \log_{e}m^n=n\log_{e}m$

$\longrightarrow \log_{a}a=1$

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