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Solve for x :4^x-3^(x-1//2)=3^(x+1//2)-2...

Solve for `x :4^x-3^(x-1//2)=3^(x+1//2)-2^(2x-1)` .

Text Solution

Verified by Experts

`4^(x)-3^(x-1/2)=3^(x+1/2) - 2 ^(2x-1)`
` or 4^(x) - 3^(x)/sqrt3 = 3^(x) sqrt3 - 4^(x)/2`
` or 3/2 xx 4^(x) = 3^(x) (sqrt3+ 1/sqrt3)`
`or 3/2 xx 4^(x) = 3^(x) xx 4/sqrt3 `
`or 4^(x-1)/4^(1//2) = 3^(x-1)/sqrt3`
` or 4^(x-3//2)= 3^(x-3//2)`
` or (4/3)^(x-3//2) = 1`
`or x-3/2 = 0`
` or x = 3//2`
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