This is solve for x:4^2x=8^3x-4

Question

I need help for the above question please :4ˆ²Χ=8^3Χ-4

Answer 1

4^(2x) = 8^(3x-4) <==Is this what you want to solve?

Change to the common base 2,

2^(4x) = 2^(9x-12), since 4 = 2^2, and 8 = 2^3

So, 4x = 9x-12

x = 12/5 <==Answer

Answer 2

Hi,

 

The essential formula here is to remember that for any a, b, and c, (a^b)^c=a^b*c. So, for example, (2³)⁴=2^3*4=2¹².

 

This problem then wants us to realize that 4=2² and 8=2³. (In all these sorts of power problems, a good tip is to try to make all the power bases equal.) We then get (2²)^2x=(2³)^(3x-4), which by our formula leads to 2^(2*2x))=2^(3*(3x–4)). Now, if 2 to the power of two things is equal, those two things must be equal, so we can conclude 2*2x=3*(3x–4). The rest is algebra that I'm sure you know:

 

4x=9x–12

5x=12

x=12/5=2.4.

 

Hope that helps!