Question

Find the value of x in the following :​

Answer 1

Solution:-

$\sf {\underline{ ★According \: to \: the \: question: }} \: \: {\boxed{ {5}^{x} \times {5}^{ - 8} = {5}^{ - 3} }} \\ \\ \tt ⟼so \: here \: we \: use \: the \: law : \: \pink{ {a}^{m} \times {a}^{n} = {a}^{m + n} } \\ \\ \sf \blue{★let's \: start : } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ : ⟹  \sf {5}^{x} \times {5}^{ - 8} = {5}^{ - 3} \\ \\ : ⟹  \sf {5}^{x - 8} = {5}^{ - 3} \: \: \: \: \: \: \: \\ \\ \sf \: : ⟹ \sf x - 8 = - 3 \: \: \: \: \: \: \\ \\ \sf: ⟹x = - 3 + 8 \: \: \: \\ \\ \sf: ⟹x = + 5 \: \: \: \: \: \: \: \: \: \: \: \:$

$\blue{\underline{\boxed{\purple{\sf{\therefore \:x=5}}}}}$

hope this helps.!!

Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

Given:

• $5^x \times 5^{-8} = 5^{-3}$

To Find:

• Value of x

Solution:

$5^x \times 5^{-8} = 5^{-3} \\ According\:to\:laws\:of\:exponents, \\ a^x \times a^y => a^{x+y} \\ So,\\ 5^x \times 5^{-8} = 5^{-3} \\ \implies 5^{x + (-8)} = 5^{-3} \\ \implies 5^{x-8} = 5^{-3} \\ As\:the\:bases\:are\:same,\:we\:compare\:the\:powers, \\ \implies x - 8 = -3 \\ \implies x = -3 + 8 \\ \implies \bold{x = -5}$

Concept used:

• $a^x \times a^y => a^{x+y}$

Hope it helps!