can someone help me answer this question, i think you need to use logs?

Question

4 ^x-3 = 8 ^2x

Answer 1

You can use logs or you can convert everything to a common base (which, even though it is not evident, is the same thing).

Use the fact that 4 = 2^2 and 8=2^3

Then
4^x-3 = 8^2x

becomes (2^2)^(x-3) = (2^3)^2x

Rule of exponents raised to power: multiply the exponents:

2^(2*(x-3)) = 2^(3*2x)
2^(2x-6) =2^(6x)

For these two expressions to be equal, their exponents must be equal. On the left you have 2 raised to a power; on the right you have 2 raised to a power. The powers must be equal.

(this is the same as taking logs in base 2)

2x-6 = 6x
-6 = 4x
-(6/4) = x = -1.5

Check

4 ^x-3 = 8 ^2x

4^(-1.5-3) = 4^(-4.5) = 1/512

8^(2*-1.5) = 8^(--3) = 1/512

OK

Answer 2

take the log of both sides
log(4^x-3)=log(8^2x)
exponents come out as coefficients
(x-3)log(4)=2x(log (8))
since 4=2^2 and 8=2^3
2(x-3)log(2)=6x(log(2)) we can divide out log2 from both sides
2x-6=6x
-6=4x
x=-3/2
I want to check this;
4^(-3/2-3)=8^(2*-3/2)
1/(4^(4 1/2)) =? 8^(-3)
1/2^9 = 1/(2^3)^3
1/512=1/512 check, sort of.
I'm sorry you can do this more compactly, but I don't use a calculator where I don't need the decimal expansion.

Answer 3

For those people who hate logarithms, you can simply find a common base and solve for x in the exponents.

4^x-3=2^2(x-3)
8^2x=2^3(2x)

That means 2(x-3)=3(2x)

2x-6=6x
4x=-6
x=-3/2

Answer 4

4 ^x-3 = 8 ^2x
=2^2(x-3)=2^3(2x) because 4=2^2 and 8=2^3

2^2x-6=2^6x
base are same soo exponents are equal
2x-6=6x
4x=-6
x=-6/4 = -3/2

Answer 5

4^(x-3) = 8^(2x)

since 4 is x^2 and 8 is 2^3...
2^(2(x-3)) = 2^(3(2x))

2(x-3) = 3(2x)

2x-6 = 6x

4x = -6

x = -3/2

4^(-3/2 -3) = 1/512
8^(2*-3/2) = 1/512