How do you solve the equation $$e^{x+6}+5=7$$ ?

Subtract 5 from both sides: $$e^{x+6} = 2$$ . Then take the natural logarithm: $$x + 6 = \text{ln}(2)$$ , so $$x = \text{ln}(2) - 6$$ .

How do you solve the equation $$6^x=80$$ ?

Take the logarithm of both sides: $$x \times \text{log}(6) = \text{log}(80)$$ . Then, $$x = \frac{\text{log}(80)}{\text{log}(6)}$$ .

Condense the expression $$2\text{log}_6a+\text{log}_6b-3\text{log}c$$ to a single logarithm.

Using properties of logarithms, it condenses to $$\text{log}_6igg(\frac{a^2b}{c^3}igg)$$ .

Evaluate $$\text{log}_2(32)$$ .

Since $$2^5 = 32$$ , we have $$\text{log}_2(32) = 5$$ .

How do you solve the equation $$4^x-5=12$$ ?

Add 5 to both sides: $$4^x = 17$$ . Then take the logarithm: $$x \times \text{log}(4) = \text{log}(17)$$ , so $$x = \frac{\text{log}(17)}{\text{log}(4)}$$ .

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 logarithms and exponents?

Logarithms are the inverse operations of exponentiation. If $$b^y = x$$ , then $$\text{log}_b(x) = y$$ .

What is the base of natural logarithms?

The base of natural logarithms is $$e$$ , approximately equal to 2.71828.

What is the value of $$\text{log}_2(8)$$ ?

Since $$2^3 = 8$$ , we have $$\text{log}_2(8) = 3$$ .

Logarithm Properties and Solving Exponential and Log Equations Flashcards

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What is the definition of a logarithm?

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