Question

\(\frac{25}{5^x}\)=\(\frac{1}{125}\)

\(2^x\)+\(2^{x+3}\)=288

\(^{\left(2x-1\right)^4}\)=81

 

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Answer 1

\(\frac{25}{5^x}=\frac{1}{125}\Rightarrow25.125=5^x.1\)

\(3125=5^x\)

\(5^5=5^x\)

\(\Rightarrow x=5\)

Answer 2

25/5^x=25/5^5

2^8+2^2+3=288

(2x-1)^4=3^4

2x-1=3

2x=4

x=2

Answer 3

\(a,\frac{25}{5^x}=\frac{1}{125}\Rightarrow\frac{5^2}{5^x}=5^{-3}\Rightarrow5^{2-x}=5^{-3}\Rightarrow2-x=-3\Rightarrow x=5\)

b, \(2^x+2^{x+3}=288\Rightarrow2^x+2^x.2^3=288\Rightarrow2^x\left(1+8\right)=288\Rightarrow2^x.9=288\Rightarrow2^x=32=2^5\Rightarrow x=5\)

c, \(\left(2x-1\right)^4=81\Rightarrow\left(2x-1\right)^4=3^4\Rightarrow2x-1=3\Rightarrow2x=4\Rightarrow x=2\)