Solve the exponential equation. Express irrational solutions as decimals correct

djeljenike

djeljenike

Answered question

2021-09-20

Solve the exponential equation. Express irrational solutions as decimals correct to the nearest thousandth.
5x3=32x
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is ______.
B. The solution is the empty set.

Answer & Explanation

Delorenzoz

Delorenzoz

Skilled2021-09-21Added 91 answers

Step 1
The given exponential equatiion is 5x3=32x.
Step 2
5x3=32x
ln(5x3)=ln(32x) [If f(x)=g(x), then lnf(x)=lng(x)]
(x3)ln(5)=2xln(3) [loga(xb)=bloga(x)]
ln(5)x3ln(5)=2xln(3)
(ln(5)2ln(3))x=3ln(5)
x=3ln(5)ln(5)2ln(3)
x=8.21439
x=8.214 [Rounded to nearest thousandth]
Thus, the solution set is -8.214

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