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

Emeli Hagan

Emeli Hagan

Answered question

2021-10-08

(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
e0.4x=8

Answer & Explanation

Anonym

Anonym

Skilled2021-10-09Added 108 answers

Step 1
Given exponential equation is e0.4x=8
To find:
(a). The exact solution of the exponential equation in terms of logarithms.
(b). Using calculator to find approximation to the solution.
Solution:
We know that if ax=n then x=logan
We have e0.4x=8 then:
0.4x=ln8       [lnx  means its base is e]
x=ln80.4
x=52ln8
Therefore, solution is terms of logarithm is x=52ln8
Step 2
(b).
We have, ln8=2.079441
Therefore,
x=52ln8
=52(2.079441)
=10.3972052
=5.198602
Hence, solution is 5.198602.

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