Logarithm of a Product Quiz

Evaluating Logarithms

• The value of log10 (1/10000) is -4, since 10^(-4) = 1/10000.

Properties of Logarithms

• If log36 6 = x, then x = 1/2, since 6^(1/2) = 36.

Simplifying Logarithmic Expressions

• log2 12 - log2 34 = log2 (12/34) = log2 (6/17), by the quotient rule of logarithms.

Logarithmic Equations

• If log3 5 = 1.465, then log3 0.6 = -1.465, since 3^(-1.465) = 0.6.

Exponential Equations

• If x = log3 27, then 3^x = 27, so x = 3, since 3^3 = 27.

• If x = log2 (1/4), then 2^x = 1/4, so x = -2, since 2^(-2) = 1/4.

• If x = log5 125, then 5^x = 125, so x = 3, since 5^3 = 125.

Exponential Equations with Variable Base

• If 2 = logx (16), then x^2 = 16, so x = 4, since 4^2 = 16.

Change of Base Formula

• The rule that relates logarithms in one base to logarithms in a different base is the change of base formula: loga x = logb x / logb a.

Applications of Logarithms

• If log10 3 = 0.47712 and log10 7 = 0.84510, then log3 7 = (log10 7) / (log10 3) = 0.84510 / 0.47712.

• If log10 5 = 0.69897, then log2 5 = (log10 5) / (log10 2) = 0.69897 / (log10 2).

• If loge 3 = 1.09861, then the value of loge 3 is 1.09861.