Question

fins the value of n if 2^n+1 5^n=200​

Answer 1

${\large{\underbrace{\underline{\bf{Question:-}}}}}$

Find the value of 'n' if $2^{n}$ + $5^{n}$ = 200.

${\large{\underbrace{\underline{\bf{Answer:-}}}}}$

$2^{n} + 5^{n}$ = 200

$[(2)(5)]^{n}$ = 200

$10^{n}$ = 200

n = $\frac{200}{10}$

∴ n = 20

★ More to know about laws of exponents -

• $a^{m}$ ×$a^{n} = a^{m + n}$

• $(a^{m})^{n} = a^{mn}$

• $a^{0} = 1$

• $a^{-n} = an$

• $(a^{m} b^{m}) = (ab)^{m}$

• $(\frac{a}{b})^{x} = \frac{a^{x} }{b^{x} }$

• $a^{x} ÷ a^{y} = a^{xy}$

Hope this helps uh! ♡