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

Find the midpoint of the segment with the following endpoints. (7,-6) and (4, -10)

Firlakuza [10]

Answer:

(5.5,-8)

Step-by-step explanation:

(7 + 4)/2 = 5.5

(-6 + -10)/2 = -8

8 0

2 years ago

1. Two students went to McDonald's. They each bought the same snack, which included a shake

Sindrei [870]

Answer:

12-2=10 b=10

Step-by-step explanation:

6 0

2 years ago

(0- (-3))×(-1+5)÷(2- (-2)) due today pls answer

Stella [2.4K]

Answer:

2 days late

Step-by-step explanation:

5 0

2 years ago