When we evaluate a logarithm, we are finding the exponent, or power x, that the base b, needs to be raised so that it equals the argument m. The power is also known as the exponent.

$5^2 = 25 \to \log_5(25) = 2$

The value of b must be positive and not equal to 1

The value of m must be positive

If 0 < m < 1, then x < 0

A logarithmic equation is an equation with a variable that includes one or more logarithms.

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Explanation:

Logarithms, or log for short, basically undo what exponents do.

When going from $5^2 = 25$ to $\log_5(25) = 2$ , we have isolated the exponent.

More generally, we have $b^x = m$ turn into $\log_b(m) = x$

When using the change of base formula, notice how

$\log_b(m) = \frac{\log(m)}{\log(b)}$

If b = 1, then log(b) = log(1) = 0, meaning we have a division by zero error. So this is why $b \ne 1$

We need b > 0 as well because the domain of y = log(x) is the set of positive real numbers. So this is why m > 0 also.

5 0

2 years ago

A: A circle has a circumference of 45 cm. What is the BEST estimate of the circle’s diameter?

dedylja [7]

Answer:

Step-by-step explanation:

d=c/pi

45/pi=14

6 0

3 years ago

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