Introduction to Logarithms

Express log₂32 = 5 in exponential form.

• 5² = 32

• 2³² = 5

• 2⁵ = 32

• 32⁵ = 2

Write 10^x = y in logarithmic form.

• log(y) = x

• log_x10 = y

• log_y(x) = 10

• log(x) = y

Express x^y = m in logarithmic form.

• log_mx= y

• log_xm = y

• log_ym = x

• log_yx = m

Express log_x(4) = m + 1 in exponential form.

• x⁴ = m + 1

• 4^x = m + 1

• x^m+1 = 4

• 4^m+1 = x

Evaluate log₅125.

• 1

• 2

• 3

• 25

Evaluate log₂(1/2).

• -1/2

• -1

• 1

• -2

Evaluate log_b1, where b>1.

• 0

• 1

• 10

• undefined

Evaluate log_bb, where b>1.

• 0

• 1

• 10

• undefined

Evaluate log_aa³.

• 3a

• 1

• 3

• a³

Evaluate 3log_bb⁴, where b>1.

• 3

• 4

• 7

• 12