1. ## check work2

1. if $3^{2x-3}=27$

x=2

2. if $2^{x-1}= \frac{1}{16}$

x=5

3. if $2^{x+2}-2^x=12
$

x=-2

4. if $300(1.05)^n=600$

n=2.78

5. to solve $3^{x+2}-3^x=216$ you must use the logarithmic method

2. Originally Posted by william
1. if $3^{2x-3}=27$

x=2 <<< No

2. if $2^{x-1}= \frac{1}{16}$

x=5 <<< No

3. if $2^{x+2}-2^x=12
$

x=-2 <<< No

4. if $300(1.05)^n=600$

n=2.78 <<< No

5. to solve $3^{x+2}-3^x=216$ you must use the logarithmic method
How did you do these calculations?

Obviously you need a lot of help. But we must know where and why you've made the mistakes. Otherwise we can't help you sufficiently.

I'll take #5:

$3^{x+2}-3^x=216~\implies~9\cdot 3^{x}-3^x=216 ~\implies~8 \cdot 3^x=216 ~\implies~3^x=27~\implies~x=3$

3. Originally Posted by earboth
How did you do these calculations?

Obviously you need a lot of help. But we must know where and why you've made the mistakes. Otherwise we can't help you sufficiently.

I'll take #5:

$3^{x+2}-3^x=216~\implies~9\cdot 3^{x}-3^x=216 ~\implies~8 \cdot 3^x=216 ~\implies~3^x=27~\implies~x=3$

for 1. x=2
2. x=-3
3. x=2
4. n=0.30

4. Originally Posted by william
1. if $3^{2x-3}=27$

x=2

2. if $2^{x-1}= \frac{1}{16}$

x=5

3. if $2^{x+2}-2^x=12
$

x=-2

4. if $300(1.05)^n=600$

n=2.78

5. to solve $3^{x+2}-3^x=216$ you must use the logarithmic method
Originally Posted by william

for 1. x=2
2. x=-3
3. x=2
4. n=0.30
No, x still isn't 2.
In this case note that 27 = 3^3

2. Yes

3. Yup

4. nay

Divide both sides through by 300:

$1.05^n = 2$

5. Originally Posted by william

for 1. x=2
...
You can check yourself if you've got the correct solution:

Plug in the value of x into the original equation. If you get the same value on both sides of the equation your solution is OK. If not then ...

$3^{2x-3}=27$ plug in x = 2 (that's your solution!):

$3^{2\cdot 2-3}=27~\implies~3^1 = 27~\implies~3 \neq 27$

6. Originally Posted by e^(i*pi)
No, x still isn't 2.
In this case note that 27 = 3^3

2. Yes

3. Yup

4. nay

Divide both sides through by 300:

$1.05^n = 2$
so 1. x=3

4. x=14.21

7. Originally Posted by william
so 1. x=3

4. x=14.21
To check do what earboth suggested in post 5 but I get those from my calculations