Question

1.What values could replace the "?" in these equations to make them true?

2. How would you explain to a friend who doesn't know about logarithms what the equation

LaTeX: \log_{10}x\:=\:y
log
10
⁡
x
=
y

says about x and y?

Answer 1

Answer:

Remember that logarithms are inverse of exponentials. That means the result of the logarithm is equal to the exponent of a power with the same base.

1. (a)

$log_{10} (10)=1$

Notice that the result is one beacuse $10^{1}=10$

(b)

$log_{10}(10000)=4$

Because $10^{4}=10000$

(c)

$log_{10}(?) =7 \implies 10^{7} =10000000$

So, $log_{10}(10000000)=7$

2.

I would say to thim that $x$ and $y$ are variables of the logarithm, which be solved by imagine the logarithm as an exponential like

$log_{10} (x)=y \implies 10^{y}=x$

In other words, the $y$ is the exponent and the $x$ is the result of the exponential.