Question

Erika is working on solving the exponential equation 50x = 17; however, she is not quite sure where to start. Using complete sentences, describe to Erika how to solve this equation.

Answer 1

@phi

Answer 2

you should use ^ to show exponents.
like so:
50^x = 17

or the equation editor
\[ 50^x = 17 \]

Answer 3

its 50^x by the way

Answer 4

yea sorry

Answer 5

exponents and logs go together , so you have to remember that
(they "undo" the other)

here is the rule you want to remember:
\[ \log\left( a^b\right)= b \log(a) \]

Answer 6

ok

Answer 7

so do i put that it the form you showed?

Answer 8

you have an equation. if you do the "same thing" to both sides
it will stay equal

in this case, "take the log" of both sides
for example , if you had
2^x = 8
take the log means write
\[ \log(2^x) = \log(8) \]

Answer 9

log(50^x)=log(17)?

Answer 10

exactly.
now on the left side, we use the "rule" (or property of logarithms)
\[ \log\left( a^b\right)= b \log(a) \]
to rewrite the left side
can you do that ?

Answer 11

\[x \log 50 = \log 17\]

Answer 12

?

Answer 13

yes. looks good.
even though it looks complicated, log(50) is a number
we can divide both sides by the same number i.e. by log(50)
\[ x \frac{\log(50)}{\log(50)} = \frac{\log(17)}{\log(50)}\]

on the left side log50 divided by itself is 1
we get
\[ x = \frac{\log(17)}{\log(50)}\]

Answer 14

so thats the final answer?

Answer 15

you could use a calculator, and find a decimal value.
but yes, that is the answer.
x is about 0.72423228

type into google:
50^0.72423228 =
and you should get something close to 17