How do you solve $$\text{log}_b(x) = y$$ for x?

To solve $$\text{log}_b(x) = y$$ , rewrite it in exponential form: $$x = b^y$$ .

How do you find the inverse of $$g(x) = 3^{(x+2)} - 4$$ ?

To find the inverse, set $$y = 3^{(x+2)} - 4$$ , solve for $$x$$ , and express it as $$g^{-1}(x) = \text{log}_3(x + 4) - 2$$ .

What is the solution to $$\text{log}_5(2x + 11) = 3$$ ?

To solve, rewrite in exponential form: $$2x + 11 = 5^3$$ , which simplifies to $$x = 57$$ .

How do you solve $$3^{\frac{x}{5}} = 27$$ ?

Rewrite 27 as $$3^3$$ , so $$\frac{x}{5} = 3$$ , leading to $$x = 15$$ .

What is the definition of an exponential function?

An exponential function is a mathematical function of the form $$f(x) = a \times b^x$$ , where $$a$$ is a constant, $$b$$ is the base, and $$x$$ is the exponent.

What is the relationship between exponential and logarithmic functions?

Exponential functions and logarithmic functions are inverses of each other. If $$y = a^x$$ , then $$x = \text{log}_a(y)$$ .

What is the value of $$\text{log}_7(343)$$ ?

Since $$343 = 7^3$$ , it follows that $$\text{log}_7(343) = 3$$ .

What is the value of $$\text{log}_7(49) + \text{log}_7(7)$$ ?

Since $$49 = 7^2$$ and $$\text{log}_7(7) = 1$$ , it follows that $$\text{log}_7(49) + \text{log}_7(7) = 2 + 1 = 3$$ .

Exponential & Log Review Flashcards

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FLASHCARD QUESTION

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What is the definition of a logarithm?

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