Question

Solve for x in the following equation:
4 · (125^x/3) − 310536 = 1964
how do i get ride of the power x/3?

Answer 1

first add 310536
to isolate the term with 1/3 expnent

Answer 2

then you can cube both sides

Answer 3

4*125^x/3=33020
do I multiply the 125 by 4? first

Answer 4

no, you can't and how is it 33020 ?
i get 312500

Answer 5

I missed a number, sorry.

Answer 6

(125^(x/3)) is one term, to isolate it, you'll have to divide by 4 on both sides.

Answer 7

125^x/3=78125

Answer 8

yes
now lets take log on both sides

Answer 9

use the property that
log A^B = B log A
log 125^(1/3) =...?

Answer 10

so log 125^(x/3)=3logx

Answer 11

try again? where did 125 go ?
note that the exponent becomes the co-efficient
log A^B = B log A
log 125^(1/3) =...?

Answer 12

A = 125
B = 1/3

Answer 13

why not B=x/3 and um, I'm lost

Answer 14

yep B = x/3 sorry.

Answer 15

so… it'll be x/3log125 but then what happened to the 78125?

Answer 16

yeah typo
log 125^(x/3) =...

Answer 17

yes
we take log both sides
so we get
(x/3) log 125 = log 78125
got this ?

Answer 18

why does the log go on both sides?

Answer 19

sorry about my questions, I am trying to understand

Answer 20

its good that you're trying to understand :)
what we do on one side we must do on other side too. so that the equation remains unchanged
so if we take log, we need to take log on both sides.

Answer 21

then this is where the C=D comes into play right?

Answer 22

At one point you had the equation: 125^x/3=78125
The x/3 is an exponent. We want to bring it down.
And the way to do that is to take the log.
But what we do on the left we have to do on the right too in order to keep the equation in tact.

Answer 23

no, here we have a co-efficient with the log
its not like log C = log D (so you can say C=D)
here, its like
a logC = log D

Answer 24

we have
(x/3) log 125 = log 78125
right ?
we need to isolate the x
start by dividing log 125 on both sides.

Answer 25

We need to solve for x. In the equation (x/3) log 125 = log 78125 everything else is a constant. 3 is a number, log(125) is a number, log(78125) is a number. the calculator will tell you what it is. So what should be done to isolate x? Divide both sides by the n umber log(125). Then multiply both sides by the number 3.

Answer 26

x/3=625?

Answer 27

what did your calculator give you for this ?
log 78125/ log 125 =..

Answer 28

i think you just did 78125/125

Answer 29

i can not utilize a calculator for this assignment i have to explain it step by step and show all my work, making side notes as well. so thats exactly what i did divide.

Answer 30

was that wrong?

Answer 31

yeah
x/3 log 125 = log 78125
right ?
so, x/3 = log 78125 / log 125

Answer 32

78125 = 5^7
125 = 5^3

Answer 33

um, where did the 5^7 come from and the 5^3

Answer 34

if i say 8, how would you know its 2^3 ?

Answer 35

78125 = 5*5*5*5*5*5*5 = 5^7

Answer 36

yes but how did you go from x/3=625 to what your doing?

Answer 37

x/3 = 625 is incorrect

Answer 38

x/3 log 125 = log 78125
right ?
so,
x/3 = log 78125/log 125
got till here ?

Answer 39

yes

Answer 40

so,
x/3 = log 5^7 / log 5^3

Answer 41

um, ok…

Answer 42

now since we know
log A^B = B log A
log 5^7 = 7 log 5

Answer 43

what about log 5^3 ?

Answer 44

3 log 5

Answer 45

yes

Answer 46

x/3 = 7 log 5 / 3log 5
what gets cancelled ?

Answer 47

log5?

Answer 48

yep
x/3 = 7/3
you can find x from here
but did u get all steps till here ?

Answer 49

yea mostly, so x=7 :)

Answer 50

yes! :)