Expand the expression: log 8 x + log 8 y + 5log 8 z

log 8 x + log 8 y + 5log 8 z = log 8 (xy) + log 8 (z^5) = log 8 (xyz^5).

Write the expression log 6 3 + log 6 2 as one logarithm.

log 6 3 + log 6 2 = log 6 (3*2) = log 6 6 = 1.

Simplify the expression: $$\text{log}_5(3) + \text{log}_5(r) - \text{log}_5(w)$$

$$\text{log}_5igg(\frac{3r}{w}igg)$$ .

What is the product rule for logarithms?

The product rule states that $$\text{log}_b(mn) = \text{log}_b(m) + \text{log}_b(n)$$ .

What is the quotient rule for logarithms?

The quotient rule states that $$\text{log}_bigg(\frac{m}{n}igg) = \text{log}_b(m) - \text{log}_b(n)$$ .

What is the power rule for logarithms?

The power rule states that $$\text{log}_b(m^p) = p \times \text{log}_b(m)$$ .

If $$\text{log}_b(x) = y$$ , what is the equivalent exponential form?

The equivalent exponential form is $$b^y = x$$ .

What is the value of log 10 1?

log 10 1 = 0, because 10 0 = 1.

What is the value of log 10 10?

log 10 10 = 1, because 10 1 = 10.

What is the significance of the base in a logarithm?

The base of a logarithm determines the rate at which the logarithmic function grows. Common bases are 10 (common logarithm) and e (natural logarithm).

Logarithms Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

2.

FLASHCARD QUESTION

Front

What is the relationship between logarithmic and exponential functions?

Back

3.

FLASHCARD QUESTION

Front

Expand the expression: log₈x + log₈y + 5log₈z

Back

log₈x + log₈y + 5log₈z = log₈(xy) + log₈(z^5) = log₈(xyz^5).

4.

FLASHCARD QUESTION

Front

Write the expression log₆3 + log₆2 as one logarithm.

Back

log₆3 + log₆2 = log₆(3*2) = log₆6 = 1.

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the change of base formula for logarithms?

Back

7.

FLASHCARD QUESTION

Front

Convert the exponential equation 10⁴ = 10000 into logarithmic form.

Back

log₁₀ 10000 = 4.

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