Solve the following equations:$ 3^{x-1} \times 5^{2 y-3}=225 $

Given:

\( 3^{x-1} \times 5^{2 y-3}=225 \)

To do: 

We have to solve the given equation.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

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

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$

Therefore,

$3^{x-1} \times 5^{2 y-3}=225$

$\Rightarrow 3^{x-1} \times 5^{2 y-3}=(15)^{2}$

$\Rightarrow 3^{x-1} \times 5^{2 y-3}=(3 \times 5)^{2}$

$\Rightarrow 3^{x-1} \times 5^{2 y-3}=3^{2} \times 5^{2}$

Comparing both sides, we get,

$x-1=2$

$\Rightarrow x=2+1=3$

$2 y-3=2$

$\Rightarrow 2 y=2+3=5$

$\Rightarrow y=\frac{5}{2}$

The values of $x$ and $y$ are $3$ and $\frac{5}{2}$ respectively.      

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Simply Easy Learning

Updated on: 10-Oct-2022

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