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(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

(1) Simplify Log2[27/4]-Log2[9/8]+Log2[1/24]. (2)What is Log7[49a]-Log10[0.01]? (3) Solve-example-1
User SlimJim
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1 Answer

10 votes
10 votes

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,


\begin{gathered} u=(30\pm√(30^2-4*9*25))/(2*9) \\ u=\frac{30\operatorname{\pm}√(900-900)}{18} \\ u=(30)/(18)=(5)/(3) \end{gathered}

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.

User Terry Wilcox
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