How do you solve the equation $$12^{2x-10} = 1$$ ?

To solve $$12^{2x-10} = 1$$ , recognize that $$1 = 12^0$$ . Therefore, set the exponents equal: $$2x - 10 = 0$$ , leading to $$x = 5$$ .

What is the domain of the function $$f(x) = 12^x$$ ?

The domain of the function $$f(x) = 12^x$$ is all real numbers, represented as $$(-\text{∞}, \text{∞})$$ .

How do you solve $$8^{x+1} = 3$$ ?

Take the logarithm of both sides: $$x + 1 = \frac{\text{log}(3)}{\text{log}(8)}$$ , leading to $$x = -0.472$$ .

What is the process to solve $$6^x = 80$$ using logarithms?

Take the logarithm of both sides: $$x = \frac{\text{log}(80)}{\text{log}(6)}$$ , which approximates to $$2.4457$$ .

Convert the logarithmic equation $$\text{log}_x 25 = 3$$ into exponential form.

The exponential form is $$x^3 = 25$$ .

What is the inverse relationship between exponential and logarithmic functions?

Exponential functions and logarithmic functions are inverses of each other. For example, if $$y = b^x$$ , then $$x = \text{log}_b y$$ .

How do you express $$b^x = a$$ in logarithmic form?

The logarithmic form is $$\text{log}_b a = x$$ .

What is the value of $$\text{log}_{10} 100$$ ?

The value is 2, since $$10^2 = 100$$ .

How do you solve $$2^{x} = 16$$ ?

Recognize that $$16 = 2^4$$ , so set the exponents equal: $$x = 4$$ .

What is the change of base formula for logarithms?

The change of base formula is $$\text{log}_b a = \frac{\text{log}_k a}{\text{log}_k b}$$ for any base $$k$$ .

How do you simplify $$\text{log}_b (xy)$$ ?

Using the product property of logarithms, $$\text{log}_b (xy) = \text{log}_b x + \text{log}_b y$$ .

What is the value of $$\text{log}_2 32$$ ?

The value is 5, since $$2^5 = 32$$ .

How do you solve $$3^{2x} = 9$$ ?

Recognize that $$9 = 3^2$$ , so set the exponents equal: $$2x = 2$$ , leading to $$x = 1$$ .

Solving Exponential Equations Flashcard

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