SOLUTION: Solve for x. ln(2x+1)+6=13 Give your answer correct to four decimals.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve for x. ln(2x+1)+6=13 Give your answer correct to four decimals.       Log On


   



Question 877781: Solve for x.
ln(2x+1)+6=13
Give your answer correct to four decimals.

Found 2 solutions by Fombitz, cigany29:
Answer by Fombitz(32388) About Me  (Show Source):
Answer by cigany29(23) About Me  (Show Source):
You can put this solution on YOUR website!
use log definition a=ln%28e%5Ea%29
6=ln%28e%5E6%29 , 13=ln%28e%5E13%29
ln%282x%2B1%29+%2Bln%28e%5E6%29=ln%28e%5E13%29
for logs with the same base, use definition
ln%28%282x%2B1%29e%5E6%29=ln%28e%5E13%29
when logs have the same base log%28b%2C%28f%28x%29%29%29=log%28b%2C%28g%28x%29%29%29 where f%28x%29=g%28x%29
so
%282x%2B1%29%28e%5E6%29=%28e%5E13%29
now solve for x
%282x%2B1%29%28e%5E6%29=%28e%5E13%29
2x%28e%5E6%29+%2B%28e%5E6%29=%28e%5E13%29
2x%28e%5E6%29=%28e%5E13%29-%28e%5E6%29
2x=%28%28e%5E13%29-%28e%5E6%29%29%2F%28e%5E6%29
x=%28%28e%5E13%29-%28e%5E6%29%29%2F2%28e%5E6%29
verify:
substitute x=%28%28e%5E13%29-%28e%5E6%29%29%2F2%28e%5E6%29 into original equation ln%282x%2B1%29%2B6=13+
ln%282%28%28e%5E13%29-%28e%5E6%29%29%2F2%28e%5E6%29%2B1%29%2B6=13%29
=+%28ln%282%28548.8165%29%29%2B6%29=13%29+
=%28ln%281097.633%29%29%2B6=13
=7.000%2B6=13
=13=13