SOLUTION: solve the equation. Round your answers to the nearest hundredth. 9+1.95^x=40

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: solve the equation. Round your answers to the nearest hundredth. 9+1.95^x=40       Log On


   

Question 38630: solve the equation. Round your answers to the nearest hundredth.
9+1.95^x=40

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
This is an exponential equation, so you will have to take the log or ln of each side of the equation to convert it from an exponential equation to an ordinary linear equation. First subtract 9 from each side:
1.95%5Ex+=+31

Now, take the ln of each side. By the way, taking the log of each side works equally well and gives exactly the same answer!
+ln+1.95%5Ex+=+ln+31

By the third law of logarithms ln+M%5Ex+=+x+%2A+ln+M
x+%2Aln+1.95+=+ln+31

Divide each side by ln 1.95:
%28x%2Aln+1.95%29%2F%28ln+1.95%29+=+%28ln+31%29%2F%28ln+1.95%29+
x+=+%28ln+31%29%2F%28ln+1.95%29+ = 5.142 approximately.
Final answer rounded to nearest tenth = 5.1

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