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Fudgin [204]
1 year ago
10

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

Mathematics
1 answer:
Feliz [49]1 year ago
7 0

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+66x=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!

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