Question

hwlp

Answer 1

As you can easily see, you're working with 2 different bases here.
Note that base 100 is the same as base 10^2.

I would change these 2 equations to exponential form. The first one becomes\[10^{\log_{10}50 }=10^{1.699}\]

Answer 2

How would you simplify the left side?

Answer 3

Can you now use this info to rewrite \[\log_{100}50? \]

Answer 4

log50/2?

Answer 5

Think:\[\log_{100}50=\log_{10^2}50 \]

Answer 6

im so confused im sorry

Answer 7

I would write\[\log_{100}50=x\] and then re-write this in exponential form. Are you able to do that?

Answer 8

log100^x=50?

Answer 9

Unfortunately, no. Your base here is 100, or 10^2. "log" does not belong in the desired "exponential form" equation. Mind thinking this over and then trying again?

Answer 10

100^x=50

Answer 11

sorry didnt mean to put the log

Answer 12

if 100^x=50, how would you find the value of x?

Answer 13

Note that y ou are given that log 50=1.699. You need to use that info to find the log to the base 100 of 50.

Answer 14

Time to stop for a sec. What part of this procedure is clear to you and what part is not?

Answer 15

i understand how its in exponential and i understand the value of x i just dont know how to find the new value

Answer 16

I had to go thru this problem several times to finally grasp what to do.

We are told that log 50 = 1.699. Just hold that for later.

Focus on "log to the base 100 of 50" or \[\log_{100}50 \]
and label it with "x=".

What do you have at this point?

Answer 17

sigh i am so confused

Answer 18

Type out the goal of this problem. Sorry for the repetition, but I want us both to be very clear about what we're looking for here.

The goal of this problem is to evaluate .... what? type it out.

Answer 19

the value of og to the base 100 of 50 when x=1.699

Answer 20

OK. Let's just say our goal is to evaluate \[\log_{100}50. \]

Answer 21

I'd like for you to name that (turn it into an equation) by prefacing it with "x="

Answer 22

log10050=x

Answer 23

\[or~x=\log_{100 } 50\]

Answer 24

yes thats what i meant

Answer 25

Now we want to eliminate that base '100'

Write a new equation: 100 = 100
(pretty obvious, no?)

Answer 26

yes

Answer 27

Now, for the left 100, use \[\log_{100}50 \] as the exponent.

Answer 28

\[100^{\log_{100}50 }.\]

Answer 29

okay

Answer 30

Can you agree with that?

Answer 31

Evaluate that. Value=?

Answer 32

Note: the expo. and log. functions are inverses of one another, so one cancels out (or undoes) the other.

Answer 33

50

Answer 34

Excellent. You began with 100 = 100 and raised the first 100 to a certain power, resulting in an overall value of 50. Now, raise the right-hand '100" to the power x.

Recall that \[\log_{100}50=x \] as we agreed earlier.

Answer 35

okay so 100^1.699???

Answer 36

No, but rather 100^x

Answer 37

You should have 50=100^x. Do you?

Answer 38

sure lol

Answer 39

Kool.

Answer 40

so now what

Answer 41

now take the common log of 50=100^x (both sides)

Answer 42

ok

Answer 43

what do you get, taking the common log of both sides of 50=100^x? Which rule or rules of logs are you going apply here?

Answer 44

gosh i really have no clue this is making it so confusing

Answer 45

sorry. At least this is almost our very last step.

Have 50=100^x.
Must take log of both sides: log 50 = x log 100. OK with that?

Answer 46

yea

Answer 47

so log50/log100

Answer 48

If log 50=xlog 100, solve for x. Hint: rewrite 100 as 10^2 first.

Answer 49

log 50=xlog ( ? )

Answer 50

what???

Answer 51

Sorry. We're on track; it's just a bit hard to follow.

50=100^x.

50=(10^2)^x. Agreed? Isn't 100=10^2?

Answer 52

yea

Answer 53

Then log 50=log (10^2). Can you simplify the right side?

Answer 54

2

Answer 55

yes. log 10^2 = 2 log 10 = 2(1) = 2. very good.

Then log 50=2x, right?

Answer 56

yes

Answer 57

solve that for x, please

Answer 58

-2log5

Answer 59

??

Answer 60

log2=-2log5

Answer 61

\[\log_{10} 50=2x\]

Answer 62

Divde both sides by 2, please

Answer 63

log5/2

Answer 64

?? unsure of how you got that.

If log 50=2x, then \[\frac{ \log_{10}50 }{ 2 }=x=?\]

Answer 65

recall that we already know the value of log 50. Substitute that value for log 50 in the above equation.

Answer 66

god i dont even know anymore

Answer 67

Review the original question we've been working on. The value of log 50 is given there.

Answer 68

log 50=?

Answer 69

1.699

Answer 70

right. What is x=1.699/2?

Answer 71

.8495

Answer 72

that's right. That's your answer.

Answer 73

woww finallyyyyy

Answer 74

Yes. As I said, I had to go thru this a couple of times too recall what to do.

Answer 75

You begin with\[\log_{100}50 \] as your unknown and name it 'x'

Answer 76

So \[\log_{100}50=x \]

Answer 77

Use the 2 sides of this equation as exponents for the equation 100 = 100. Follow me? I'm just summarizing what we've already done.

Answer 78

\[100^{\log_{100}50 }=100^{x}\]

Answer 79

OK?

Answer 80

Good idea to copy down this summary for later ref.

Answer 81

OK?

Answer 82

I was going to review this problem very quickly to help you consolidate what you've learned. Guess something else has caught your attention.

Enjoyed working with you.