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If `3^(X+1)=9^(X-2),` Find the Value of `2^(1+X)` - Mathematics

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Question

If `3^(x+1)=9^(x-2),` find the value of `2^(1+x)`

Solution

`3^(x+1)=9^(x-2)`

`rArr3^x xx3=9^x/9^2`

`rArr3^x xx3=(3^2)^x/(3^2)^2`

`rArr3^x xx3=3^(2x)/3^4`

`rArr3^4xx3=3^(2x)/3^4`

`rArr3^5=3^x`

Comparing both sides, we get

x = 5

So,

`2^(1+x)=2^(1+5)=2^6=64`

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 9 (2018 (Latest))
Chapter 2: Exponents of Real Numbers
Ex. 2.2 | Q: 13 | Page no. 26
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If `3^(X+1)=9^(X-2),` Find the Value of `2^(1+X)` Concept: Laws of Exponents for Real Numbers.
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