Question

I don't know how to do those

Answer 1

19) n = log₁₀10,000
n = 4 (10⁴ = 10,000)
21) n = log₂₀400
n = 2 (20² = 400)
23) 4 = log₃n
n = 81
log₃3 = 1; log₃(3⁴) = 4
log₃n = 4
log₃n = log₃(3⁴)
n = 3⁴ = 81

Answer 2

Logarithmic and exponential functions are the inverses of each other; that is, their x and y-ordinates are interchanged. As such, this begs the question of "how would you articulate the relationship between one another in verbal language?"

Rule 1, in logarithmic laws, state that any logarithmic function can be rewritten in exponential form.

Take the general case: $y = log_a x$
For all logarithmic laws in this form, there are several ideas and names that we need to consider.

Since their relationship between one another are inverses, we can rewrite it in another way.
For instance, the inverse of $y = a^{x}$ becomes $x = a^{y}$
Now, we still have an exponential as our inverse, but another theorem we know is that for any exponential function, its inverse will be its logarithmic function, so this begs another question: "how do I rewrite this in logarithmic form?"

Since we want y the subject, we need to consider taking the logarithm of the base.
$log_a x = log_aa^{y}}$

Thus, $log_ax = y$
But, we know that $y = a^{x}$
So, $y = a^{x}$ becomes: $x = log_ay$

And this is true for any exponential and logarithmic functions.