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Exponential Representation for Irrational Numbers

If -35x = -...

Question

If $(- \frac{3}{5})^{x} = - \frac{27}{125}$ , then find the value of $x$ .

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Solution

$(- \frac{3}{5})^{x} = - \frac{27}{125}$
$⟹ (\frac{- 3}{5})^{x} = (\frac{- 3}{5})^{3}$
Comparing, we get
$x = 3$

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Similar questions

(\sqrt{\frac{3}{5}})^{x + 1} = \frac{125}{27}

Q. Find the value of x in the following:

(\frac{3}{5})^{x} . (\frac{5}{3})^{2 x} = \frac{125}{27}

Q. Find the value of x, if:

(\frac{125}{27}) \times (\frac{125}{27})^{x} = (\frac{5}{3})^{18}

Q. Find the value of x :

{(\frac{3}{5})}^{x} {(\frac{5}{3})}^{2 x} = \frac{125}{27}

5^{x + 1} \div 25 = 125,

find the value of x.

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