Given that the log base 12 of 𝑣
plus three equals one, find the value of 𝑣.
Let’s consider this in two
different ways. The first way is to rewrite this
log in exponential form. If we know that log base 𝑏 of 𝑥
equals 𝑘, then we can rewrite that as 𝑏 to the 𝑘 power equals 𝑥. For us, that will be 12 to the
first power equals 𝑣 plus three. We know that 12 to the first power
equals 12. So we subtract three from both
sides of the equation. And we see that nine equals 𝑣 or
more commonly 𝑣 equals nine.
But is there another way we can
think about this question? Well, if we know that log base 𝑏
of 𝑏 equals one, we could rewrite one in the form log base 12 of 12, since log base
12 of 12 does equal one. And then since we’re dealing with
two logs with the same base, set equal to each other, we can say that 𝑣 plus three
is equal to 12. And again, we’ll subtract three
from both sides, to see that 𝑣 equals nine. Both methods are valid ways to
rearrange the equation to solve for 𝑣.