Question

solve by creating same bases: 1/9 = 27 ^ x-1

Answer 1

\[\frac{1}{9}=3^{-2}\]

Answer 2

\[27^{x-1}=(3^{3})^{x-1}\]

Answer 3

\[(3^{3})^{x-1}=3^{3x-3}\]

Answer 4

So:\[3^{-2}=3^{3x-3}\]

Answer 5

And -2=3x-3
1=3x
1/3=x

Answer 6

Can you please help me with one more??? PLEASE!! begging you.

Answer 7

Post it.

Answer 8

properties of logarithms: 3^x=5^x+2

Answer 9

3^x=5^(x+2)

Answer 10

\[x \log_{10}3=(x+2)\log_{10}5 \]

Answer 11

How did you get that?

Answer 12

Find the log of 3 and the log of 5 using your calculator and solve the equation.

Answer 13

\[a ^{n}=n \log_{10}a \]

Answer 14

how did you know what the variables were?

Answer 15

That is the property of law of logs. Perhaps your book uses different variables. What the variables are doesn't matter. Did you book say:
\[m ^{n}=n \log_{10}m \]

Answer 16

oh eyes!

Answer 17

yes

Answer 18

So use that property on 3^x

Answer 19

Would you not get xlog3?

Answer 20

I think my answer is wrong :/

Answer 21

What did you get?

Answer 22

4.52

Answer 23

Hang on.

Answer 24

xlog3=.477x and (x+2)log 5 = .699x+1.40

Answer 25

do you agree with that/

Answer 26

Yes!

Answer 27

Subtract .699x from both sides.

Answer 28

-.222x=1.40

Answer 29

Oh so the final answer is 1.40?

Answer 30

Now divide both sides by -.222

Answer 31

Oh so -6.31?

Answer 32

yes.

Answer 33

THANK YOU SO MUCH! seriously, you are my life-saver. Now I have one more, I don't want to make you have to show me but could I just ask you a question about it?

Answer 34

Yes

Answer 35

http://gyazo.com/8020e5d281ab10e0d5802e2690ad9794

Answer 36

I don't get if there's acertain equation I am supposed to apply because it looks so confusing.

Answer 37

This involves two laws of logs. On the left side you have the difference of two logs which is equal to the log of the quotient.

Answer 38

\[\log_{3} \frac{x+1}{x}\]

Answer 39

The right side is the property we used in the last problem.

Answer 40

\[2\log_{3}2=\log_{3}2^{2} \]

Answer 41

So now, if the logs are equal, and the bases are the same, the arguments must be equal

Answer 42

\[\frac{x+1}{x}=2^{2}\]

Answer 43

solve that equation.

Answer 44

Cross multiply

Answer 45

4x=x+1

Answer 46

3x=1
x=1/3

Answer 47

thank you so so so much!