Question

(c) 5^x5^x+1 = 125
Solve for x
​

Answer 1

$Given \: \red{ 5^x\times 5^{x+1} = 125 }$

$\implies 5^{x+x+1} = 5^{3}$

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/* By Exponential Law *

$\boxed { \pink { a^{m} \times a^{n} = a^{m+n}}}$

________________

$\implies 5^{2x+1} = 5^{3}$

$\implies 2x + 1 = 3$

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/* By Exponential Law */

$\boxed { \pink {If \: a^{m} = a^{n} \implies m = n }}$

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$\implies 2x = 3-1$

$\implies 2x = 2$

$\implies x = \frac{2}{2}$

$\implies x = 1$

Therefore.,

$\green { Value \: of \: x = 1}$

•••♪

Answer 2

$\bf{\underline{\underline{\bigstar\bigstar\: Some \: information : }}}$

$\:\:$

• ${}x}^{a} \times {x}^{b} = {x}^{a + b}}$

• ${{x}^{a} = {x}^{b} \implies a = b}$

$\:\:$

$\bf{\underline{\underline{\bigstar\bigstar\: Solution :}}}$

$\:\:$

${{5}^{x} \times {5}^{x + 1} = 125}$

${\impies {5}^{x + 1 + x} = {5}^{3}}$

${\impies {5}^{2x + 1 } = {5}^{3}}$

${\impies 2x + 1 = 3}$

${\impies 2x = 3 - 1}$

${\impies 2x = 2}$

$\displaystyle{\impies x = \frac{2}{2}}$

${\implies x = 1}$

$\:\:$

$\bold{ value \: of \: x = 1 }$