SOLUTION: How do you find a solution of the exponential equation, correct to four decimals places. 20. 10^1-x = 6^x

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: How do you find a solution of the exponential equation, correct to four decimals places. 20. 10^1-x = 6^x      Log On


   

Question 88611This question is from textbook
: How do you find a solution of the exponential equation, correct to four decimals places.
20. 10^1-x = 6^x This question is from textbook

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can use logarithms to solve exponential equations.
10%5E%281-x%29+=+6%5Ex Take the commom logarthim of both sides.
Log%5B10%5D%2810%5E%28%281-x%29%29%29+=+Log%5B10%5D%286%5Ex%29 Apply the power rule for logarithms.
%281-x%29Log%5B10%5D%2810%29+=+x%2ALog%5B10%5D%286%29 Recall that Log%5B10%5D%2810%29+=+1
%281-x%29+=+x%2ALog%5B10%5D%286%29 Add x to both sides.
1+=+x%2BxLog%5B10%5D%286%29 Factor out the x.
1+=+x%281%2BLog%5B10%5D%286%29%29 Divide both sides by 1%2BLog%5B10%5D%286%29
1%2F%281%2BLog%5B10%5D%286%29%29+=+x Evaluate this.
1%2F%281%2B0.778%29+=+x
x+=+1%2F1.778
x+=+0.56243