Solve the equation for x by first making an appropriate substitution, such as u=e^x

5e^2x-16e^x+3=0

Question

Solve the equation for x by first making an appropriate substitution, such as u=e^x

5e^2x-16e^x+3=0

campbell_st · Answer

let$$ u = e^x $$

so $$e^{2x} = (e^x)^2$$

using the power of a power index law

so you will have 

$$5u^2 - 16u + 3 = 0$$

which can be factorised.... 

(5u - 1)(u - 3) = 0

thats the hard part.. 

all you need to do is solve... 

$$e^x = \frac{1}{5}..... and ..... e^x = 3$$

use logarithms...

anonymous · Answer

It says its not right for both of them =/

anonymous · Answer

@campbell_st

campbell_st · Answer

thats correct..its not right...as you still need to find x.... 

that is what value of x when a power of e is equal to 1/5 and 3

so you need to take the base e log of both sides to get your answer... one value will be positive and one value will be negative

anonymous · Answer

Ahhh! I got it finally...thank you!