Solve each of the following equations.

Question

Solve for x. (Note: Further simplification may occur in step (b).) Write the answer in terms of natural logarithms, unless no logarithms are involved. Rewrite the answers to each individual logarithm from part (a) is written as a sum or difference of logarithms of prime numbers. Write the answer in simplest form. If the simplified answer from part (b) contains logarithms, rewrite the answer as a decimal, correct to the nearest thousandth; otherwise, simply rewrite the answer.

 

 

e^x =45

 

e^x−9=−3

 

2e^7-3x=−20

Answer 1

e^x = 45

ln e^x = ln 45

x = ln 45

 

e^x - 9 = -3

e^x = 6

ln e^x = ln 6

x = ln 6

 

2e^7-3x = -20

e^7-3x = -10

ln e^7-3x = ln -10

Not possible, e to any power is positive