pre-cal

posted by .

Find the solution of the exponential equation, correct to four decimal places.

4^(2x − 1) = 6

  • pre-cal -

    log ( a ^ n ) = n * log ( a )


    ( 2 x - 1 ) * log ( 4 ) = log ( 6 ) Divide both sides by log ( 4 )

    2 x - 1 = log ( 6 ) / log ( 4 )

    2 x = log ( 6 ) / log ( 4 ) + 1

    2 x = log ( 6 ) / log ( 4 ) + log ( 4 ) / log ( 4 )

    2 x = [ log ( 6 ) + log ( 4 ) ] / log 4

    2 x = log ( 24 ) / log ( 4 ) Divide both sides by 2

    x = [ log ( 24 ) / log ( 4 ) ] / 2

    x = log ( 24 ) / 2 log ( 4 )


    Remark:

    log ( a ) + log ( b ) = log ( a * b )

    log ( 4 ) + log ( 6 ) = log ( 6 * 4 ) = log ( 24 )

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. pre-cal

    Find the solution of the exponential equation, correct to four decimal places. 4^(2x − 1) = 6
  2. Pre-Cal Help Please!!

    Use logarithms to solve the given equation. (Round the answer to four decimal places.) 6(1.02^3x + 1) = 11 How do i find the answer after 1.03^3x +1 = (11/6) Do i put a log on 1.03 or do I do something else Thank you.
  3. Math

    Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 7^4x = 4.9
  4. pre-calculus

    solve the following logarithmic equation. be sure to reject any value of x that is not in the domain of the original logarithmic expression. give the exact answer. then, use the calculator to obtain a decimal appromiation, correct …
  5. math

    Find the solution of the exponential equation 7+(5^5x)=25 correct to at least four decimal places.
  6. Cal 1

    Use Newton's method with the specified initial approximation x1 to find x3, the third approximation to the root of the given equation. (Round your answer to four decimal places.) 1/3x^3 + 1/2x^2 + 1 = 0, x_1 = −3
  7. college algebra

    Solve the exponential equation using logarithms. Give the answer in decimal form, rounding to four decimal places. (Enter your answers as a comma-separated list.) 4x − 3 = 32x x = _____
  8. college algebra

    Solve the exponential equation using logarithms. Give the answer in decimal form, rounding to four decimal places. (Enter your answers as a comma-separated list.) 4^(x − 3) = 3^(2x) x = _____
  9. Pre-Cal

    An equation is given. (Enter your answers as a comma-separated list. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 2 cos 2θ − 1 = 0 a). Find all solutions of the equations …
  10. Pre-Cal:(Cont.)

    [Note: I've tried this problem 4 times already and still have it wrong. I know the steps to doing it but for some reason its wrong. an someone please help me get these answers for (b).] An equation is given. (Enter your answers as …

More Similar Questions