Logarithm question!?

Question

Express the given equations in logarithmic form. 1) 3^3 = 27 2) 4^-2 = 1/16 3) (81)^3/4 = 27

Answer 1

1)

3³ = 27

Apply log both sides.

log(3³) = log(27)

Apply formula : log(a^b) = b log(a)

3log(3) = log(27)

log(27) / log(3) = 3

Apply formula : log(a)/log(b) = Log_b(a)

Log₃(27) = 3

Answer 2

2)

4^-2 = 1 / 16

Apply log both sides.

log(4^-2) = log(1/16)

Apply formula : log(a^b) = b log(a)

(-2)log(4) = log(1/16)

log(1/16) / log(4) = -2

Apply formula : log(a)/log(b) = Log_b(a)

Log₄(1/16) = -2

Answer 3

3)

(81)^3/4 = 27

81^¾ = 27

Apply log both sides.

log(81^¾) = log(27)

Apply formula : log(a^b) = b log(a)

¾log(81) = log(27)

log(27) / log(81) = ¾

Apply formula : log(a)/log(b) = Log_b(a)

Log₈₁(27) = ¾