PLEASE LOG HELP

Question

question 1: 20e^3x=100

question2: 2^5x=24

Answer 1

20e^3x = 100

 

e^3x = 5                 [Divide both sides by 20]

 

ln(e^3x) = ln(5)       [Take the natural log (ln) of both sides]

 

3x = ln(5)

 

x = ln(5)/3 ≅ 0.5365

 

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2^5x = 24

 

log₂(2^5x) = log₂(24)

 

5x = log₂(2³*3) = log₂(2³) + log₂(3)

 

5x = 3 + log₂(3)

 

x = (3+log₂(3))/5 ≅ 0.917