SOLUTION: 3^x=40 e^0.04t=1500 please help me solve these... if possible...i need good step by step process

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 3^x=40 e^0.04t=1500 please help me solve these... if possible...i need good step by step process       Log On


   

Question 143204: 3^x=40
e^0.04t=1500
please help me solve these... if possible...i need good step by step process

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Use logs
Given: 3%5Ex=40
Take the log of both sides
log%283%5Ex%29+=+log%2840%29
When using logs, if the term inside parens is raised to a power, then your can 'bring the power down' as a multiplier.
x+%2A+log%283%29+=+log%2840%29+
Now get out your handy calculator and find log(3) and log(40)
x+%2A+%280.47712%29+=+1.602
Now solve for x as a one step algebra simplification
x+=+3.3576
Finally, check your answer using a calculator. Does 3^3.3576 = 40? Close enough!
For the second problem, use logs again. Except this time, use natural log (ln)
Given: e%5E%280.04t%29=1500
Take the ln of both sides
ln%28e%5E%280.04t%29%29+=+ln%281500%29+
The ln of a power of e, it just the power.
0.04t+=+ln%281500%29+
Whip out your calculator and find ln(1500) (somebody help that man!)
0.04t+=+7.313
+t+=+182.83
Check your answer using the calculator. Does it check out? You bet it does,