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

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.