(a) Find the exact solution of the exponential equation in terms of logarithms.

ankarskogC

ankarskogC

Answered question

2021-10-29

(a) Find the exact solution of the exponential equation in terms of logarithms. (b) Use a calculator to find an approximation to the solution rounded to six decimal places
4x+21+2x=50

Answer & Explanation

stuth1

stuth1

Skilled2021-10-30Added 97 answers

Step 1
An exponential equation can be converted to logarithm equation because logbx=y is equivalent to the equation x=by . To convert an equation into an exponential equation combine the exponential terms into one single term.
Then take logarithm of both sides to convert exponential to logarithm equation. Use the property of logarithms logbx=xlogb
Step 2
(a)
Given equation is 4x+21+2x=50 . SImplify and combine terms on the left hand side as exponential equation with exponential term being 4x.
4x+21+2x=50
4x+222x=50
4x+2(22)x=50
4x+24x=50
34x=50
4x=503
ln4x=ln503
x=ln503ln4
(b)
In the calculator press log button and enter 503 . Then press the divide button and press log again and enter 4 and press enter. The solution comes to be equal to 2.029447.

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