What is the power rule for logarithms?

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

How do you condense logarithmic expressions?

To condense logarithmic expressions, apply the product, quotient, and power rules to combine multiple logarithms into a single logarithm.

What is the value of $$2^x = 8$$ ?

The value of $$x$$ is 3, since $$2^3 = 8$$ .

How do you solve $$3^{3} = 3^{4x + 2}$$ for x?

Since the bases are the same, set the exponents equal: $$3 = 4x + 2$$ , which simplifies to $$x = \frac{1}{4}$$ .

What is the solution to $$2^x = 4^{x+1}$$ ?

Rewrite $$4$$ as $$2^2$$ : $$2^x = (2^2)^{x+1} = 2^{2x + 2}$$ . Set the exponents equal: $$x = 2x + 2$$ , leading to $$x = -2$$ .

What is the value of $$14^{4-6x} = 11$$ ?

Taking logarithm on both sides and solving gives $$x = 0.5$$ .

What is $$5\text{log}_a - 25\text{log}_b$$ condensed?

Using the quotient rule, it condenses to $$\text{log}igg(\frac{a^5}{b^{25}}igg)$$ .

What is $$3\text{log}_x + 4\text{log}_y + \text{log}_z$$ condensed?

Using the product rule, it condenses to $$\text{log}(x^3y^4z)$$ .

Review for test on exponential and logs Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What is the base of a logarithm?

Back

3.

FLASHCARD QUESTION

Front

What is the relationship between exponents and logarithms?

Back

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