Solve the given equation for x

Question

8^3x^+5 = (1/4)^x^-2

 

 

 

(e^x)^2 = e^4x e^6

Answer 1

Hopefully I am reading your equation correctly... 

 

The second equation is: (e^x)²=e^4x * e⁶  right?

 

If so, an exponent to an exponent can be multiplied, and exponents with like bases can be added:

e^2x = e^4x+6

 

We can simplify the right side:

e^2x = e^2(2x+3)

 

By exponent rules, we can divide e² from both sides:

e^x = e^2x+3

 

Divide both sides by e^x (the 2x will be subtracted by x due to exponent division rules)

1 = e^x+3

 

Take the natural log of both sides:

0 = x+3

 

Solve for x:

x=-3

 

 

 

Now for the first equation, do you mean (8^3x)⁵ = ((1/4)^x)^-2  ?

 

Let me know if that is the correct formatting!  

 

Thanks, 

Alyssa :)