Solve for x:

`16^(2x-3)=8^(4x+1)`

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`16^(2x-3)=8^(4x+1)`

`2^(4(2x-3))=2^(3(4x+1))`

Using logaritms:

`4(2x-3)=3(4x+1)`

`8x-12=12x+3`

`4x=-15`

`x=-15/4`

`16^(2x-3)=8^(4x+1)`

To solve, express both sides of the equation with same base. So factor 8 and 16.

`(2^4)^(2x-3)=(2^3)^(4x+1)`

Then, apply this property of exponents which is `(a^m)^n=a^(m*n)` .

`2^(4(2x-3))=2^(3(4x+1))`

`2^(8x-12)=2^(12x+3)`

Now that both sides have the same base, equate the exponents equal to each other.

`8x-12=12x+3`

Then, bring together the terms with x on one side of the equation.

`8x-8x-12=12x-8x+3`

`-12=12x-8x+3`

And, bring together the terms without x on the other side of the equation.

`-12-3=12x-8x+3-3`

`-12-3=12x-8x`

`-15=4x`

And, isolate x.

`-15/4=(4x)/4`

`-15/4=x`

**Hence, the solution to the given equation is `x=-15/4` . **

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