Hello friends, please, I need to know how to get the answer out of this exponential equation?

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Hello friends, please, I need to know how to get the answer out of this exponential equation?

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Answer 1 · 2016-11-03T03:38:43

$x = \frac{3}{4}$ $x=3/4$

Explanation:

Recall that $\sqrt{x} = x^{\frac{1}{2}}, and x^{a} \cdot x^{b} = x^{a + b}$ $sqrtx=x^(1/2), and x^a*x^b=x^(a+b)$ ,

$5^{2 x + 1} = 25 \sqrt{5}$ $5^(2x+1)=25sqrt5$
$\Rightarrow 5^{2 x + 1} = 5^{2} \cdot 5^{\frac{1}{2}} = 5^{2 + \frac{1}{2}} = 5^{\frac{5}{2}}$ $=> 5^(2x+1)=5^2*5^(1/2)=5^(2+1/2)=5^(5/2)$
$\Rightarrow 2 x + 1 = \frac{5}{2}$ $=> 2x+1=5/2$
$\Rightarrow 2 x = \frac{5}{2} - 1 = \frac{3}{2}$ $=> 2x=5/2-1=3/2$
$x = \frac{3}{2} \cdot \frac{1}{2} = \frac{3}{4}$ $x=3/2*1/2=3/4$

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Hello friends, please, I need to know how to get the answer out of this exponential equation?

1 Answer

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