Use the product rule to expand each logarithmic expression l

Use the product rule to expand each logarithmic expression log_3(3.8) = log(10y) = ln(5e^3) = log_ (7.11) = log(100 x) = ln(10 e^2) = Use the quotient rule to expand each logarithmic expression log_4(20/x) = log(100/4) = ln(x^2/4) = log_ (23/x) = log(a/100) = ln(e^s/13) = Use the power rule to expand each logarithmic expression log_6 7^8 = ln squareroot x = log (4 + x)^5 = log_6 3^9 = ln3 squareroot x = log(x + y)^10

Solution

1)

a) log₃(3*8) = log₃3 + log₃8 = 1 + log₃8

b) log(10y) = log10 + logy = 1 + logy

c) ln(5e³) = ln5 + 3lne = 3 + ln5

A) log₆(7*11) = log₆7 + log₆11

B) log(100x) = log100 + log x = 2 + log x

C) ln(10e²) = ln10 + 2lne = 2 + ln10

2)

a) log(10/x) = log10 – log x = 1 – log x

b) log(100/9) = log 100 – log 9 = 2 – 2log3

c)ln(e²/9) = 2 – ln9

A)

B)log(a/100) = log a - 2

C) ln(e³/10) = 3 – ln10