A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, if $$b^y = x$$ , then $$log_b(x) = y$$ .

How do you calculate the time to double an investment with continuous compounding?

To calculate the time to double an investment with continuous compounding, use the formula: $$t = \frac{ln(2)}{r}$$ , where $$r$$ is the interest rate.

What is the relationship between exponential and logarithmic functions?

Exponential functions and logarithmic functions are inverses of each other. If $$y = b^x$$ , then $$x = log_b(y)$$ .

How do you solve exponential equations?

To solve exponential equations, you can take the logarithm of both sides or rewrite the equation in logarithmic form.

What is the significance of the base in logarithms?

The base of a logarithm determines the rate of growth. Common bases are 10 (common logarithm) and e (natural logarithm).

How do you solve for x in equations of the form $$b^{x} = a$$ ?

To solve for x, take the logarithm of both sides: $$x = log_b(a)$$ .

What is the natural logarithm?

The natural logarithm, denoted as $$ln(x)$$ , is the logarithm to the base e, where e is approximately 2.718.

What is the common logarithm?

The common logarithm, denoted as $$log(x)$$ , is the logarithm to the base 10.

How do you apply logarithms to solve real-world problems?

Logarithms can be used to solve problems involving exponential growth or decay, such as population decline, interest calculations, and sound intensity.

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