Question

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

Answer 1

Answer:

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!