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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Step-by-step 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) = (\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 \\e 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.