SOLUTION: Please help I am really confused and could use a step by step break down. Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help I am really confused and could use a step by step break down. Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state      Log On


   

Question 251206: Please help I am really confused and could use a step by step break down.
Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this.
ln (2x + 3) = 2

Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this.
log2√x^2-4 = 1

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this.
ln (2x + 3) = 2
Find antilog (e%5Ex) of both sides
2x + 3 = 7.389
2x = 7.389 - 3
2x = 4.389
x = 4.389%2F2
x = 2.195
:
Check this: enter into your calc: ln(2(2.195)+3) ans 2.000 confirms our solution
:
:
Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this.
log2sqrt%28x%5E2-4%29+=+1
Assume you mean this is a base 2 log
Write the exponent equiv of logs
2%5E1+=+sqrt%28x%5E2-4%29
Which is:
2 = sqrt%28x%5E2-4%29
square both sides
4 = x^2 - 4
8 = x^2
x = sqrt%288%29
x = 2%2Asqrt%282%29
or
x = 2.828