Question

5^x+5^x-1=750,find x

Answer 1

5^x+5^x-1=750
5^x+5^x-1= 5⁴+5³
compare power because bases are equal
X-1= 3.= X= 4

; x=4

Answer 2

Answer:

$Value \: of \: x = 4$

Step-by-step explanation:

$Given \\5^x+5^{x-1}=750$

$\implies 5^{x}+\frac{5^{x}}{5}=750$

$By \: Exponential \:Law:\\a^{m-n}= \frac{a^{m}}{a^{n}}$

$\implies 5^{x}[1+\frac{1}{5}]=750$

$\implies 5^{x}[\frac{5+1}{5}]=750$

$\implies 5^{x}\times \frac{6}{5}=750$

$\implies 5^{x}=750 \times \frac{5}{6}$

$\implies 5^{x}= 125 \times 5$

$\implies 5^{x}=5^{3}\times 5$

$\implies 5^{x}=5^{4}$

$\implies x = 4$

$By, Exponential\: Law :\\If \: a^{m}=a^{n}\: then\: m=n$

Therefore,

$Value \: of \: x = 4$

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