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Solve the following equations: 2^(x-5)=2...

Solve the following equations: `2^(x-5)=256` (ii) `2^(x+3)=4^(x-1)`

Text Solution

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`(i):2^(x-5)=256`
`2^(x-5)=2^8`
As bases are same, we can equate the powers
`x-5=8`
`x=13`
Hence the value of `x` is found as `13`
`(ii): 2^(x+3)=4^(x-1)`
`2^(x+3)=2^(2x-2)`
By comparing powers
`x+3=2x-2`
`x=5`
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