Solve the Equation?

Question

5 * 4^(2x+1) - 10 * 4^x + 1 = 0

Note* could you please show step by step..

Answer 1

Here is one way, not sure if it's the best but it works:

4^(2x+1) = 4^2x times 4^1 so 5 * that would be 20 * 4^2x

You now have 20 * 4^2x - 10 * 4^1 + 1 = 0

Let u = 4^x. Then u^2 = 4^2x

20u^2 - 10u + 1 = 0

Use quadratic formula to get u

u = 10 +- sqrt (100 - 20) all over 40

simplified is 5 +- sq rt 5 all over 20

but u = 4^x

so 4^x = 5 +- sq rt 5 all over 20

take log of both sides

x log 4 = log ( that stuff)

divide by log 4 to get x. (There will be 2 answers, one for the + and one for the -)

I tried it and checked by graphing and it works.

Answer 2

At start 4^(2x+1)=( 4^x)^2 *4

If you call 4^x =z
you get

20z^2-10z +1= 0 a second degree equation in z


z=( 10 +-sqrt(100-80))/40 = ( 10 +-sqrt20)/40 As both roots are positive For each you should put

Example 4^x= (10+sqrt20/40

taking log x*log4 = log((10+sqrt20)/40 )

so x = log((10+sqrt20)40)/ log4 =0.2610

Do the same for the minus sign at the sqrt

Answer 3

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