Question

Solve each equation . 4^3x-3= 8^4x-4

Answer 1

x = 1

Explanation:

To solve for x in the equation,

`4^(3x-3)=8^(4x-4)`

We write each side as

`\begin{gathered} 4^(3x-3)=(2^2)^(3x-3) \\ 8^(4x-4)=\mleft(2^3\mright)^{\mleft\{4x-4\mright\}} \end{gathered}`

which gives

`(2^2)^(3x-3)=(2^3)^{\{4x-4\}}`

Now, using the property that

`(A^x)^y=A^(xy)`

we rewrite the above as

`2^(2(3x-3))=2^{3\{4x-4\}}`

Which implies

`2(3x-3)=3(4x-4)_{}`

Expanding the equation gives

`6x-6=12x-12`

Adding 6 to both sides gives

`6x=12x-12+6`
`6x=12x-6`

subtracting 12x from both sides gives

`6x-12x=-6`
`-6x=-6`

Finally, dividing both sides by -6 gives

`x=1`

which is our answer!