Question

NO LINKS!! Please help me with these notes. Part 1a​

Answer 1

Answers:

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.