Question

(1) Simplify Log2[27/4]-Log2[9/8]+Log2[1/24]. (2)What is Log7[49a]-Log10[0.01]? (3) Solve this: 9e2x-30ex+25=0 (4) If 81-2x=1/4x, find x

Answer 1

Given

The equation is given as

`9e^(2x)-30e^x+25=0`

Explanation

Solve and simplify the expression

`9e^(2x)-30e^x+25=0`

Let substitute

`e^x=u`

in the equation.

`9u^2-30u+25=0`

Solve the quadratic equation,

So the solution is

`\begin{gathered} (u-(5)/(3))^2=0 \\ u=(5)/(3) \end{gathered}`

Now find the value of x ,

`\begin{gathered} e^x=(5)/(3) \\ x=ln\text{ }(5)/(3) \end{gathered}`

Then the value of x is obtained as

`x=0.51`

Answer

Hence the solution of the equation is 0.51.