
Solve for x,
to the nearest thousandth. 
Answer

1. 


• Take the log of both
sides.
• Apply the log rule for exponents shown
above.
• Solve for x.
• Estimate answer using calculator. 
OR

• log base 5 can also be used as a solution
method
• notice how the log_{5} of 5^{x}
is really
composition and yields
x.
• notice the change of base formula used
at end 

2.



OR 

Also, log base 3 can be used. 
3. 


Also, log base 1/2 can be used as a
solution method. 

4.



OR 


5.


Since the natural log is the inverse
of the exponential function, use ln to
quickly solve this problem.

6. 


• First, get
rid of the coefficient of the exponential
term (divide by 150). • Now, proceed using ln to quickly
solve.
• Do not round too quickly. Be sure
to carry enough decimal values to allow you
to round to thousandths (in this case) for the final
answer. 

7. 


• Isolate the exponential
• Take the log of both sides
• Apply the log property
• Divide by log 4
• Estimate using calculator 

8. 


• Isolate the
exponential • Divide each side by
the coefficient of 2
• Take ln of both sides
• Remember that ln x and e^{x}
are inverse functions. 

9. 


• First, divide by the
coefficient to isolate the exponential •
Proceed as shown above. 

10. 

This question requires some additional thinking.
Because of the differing powers of e, our
previous methods will not be of much help. We
will need a different strategy with this problem.

• Remember that e^{x} • e^{x}
= e^{2x} • This
problem is really
x^{2}  4x + 3 = 0
where x = e^{x}.
• Factor
• Both solutions are answers. 
