Logarithm of a Product Quiz

What is the value of log10 (1/10000)?

If log36 6 = x, what is the value of x?

Simplify log2 12 - log2 34.

If log3 5 = 1.465, what is the value of log3 0.6?

What is the value of $x$ if $x = \log_3 27$?

What does $x = \log_2 (1/4)$ equal to?

If $x = \log_5 125$, what is the value of $x$?

For $2 = \log_x (16)$, what is the value of $x$?

What is the rule that relates logarithms in one base to logarithms in a different base?

If log10 3 = 0.47712 and log10 7 = 0.84510, what is log3 7?

Given log10 5 = 0.69897, what is log2 5?

What is the value of loge 3 if loge 3 = 1.09861?

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.

Test your understanding of logarithms of products with this quiz. Solve problems involving log properties like addition and multiplication. Practice simplifying expressions with logarithms.