# Thread: ln or log problems im confused

1. ## ln or log problems im confused

Hey guys I am new to this website and wanted some help. I would like to see the steps if possible. Thank you!

Solve for t or x. Round off 3 significant decimals
ln(t/t-2)=1
5^(t+1)=6^t
ln9x=1
2=e^(.6t)
1/5=e^(4x)
9ln x = 15
ln 3 + ln x= 1.4

2. Originally Posted by Jackie10
Hey guys I am new to this website and wanted some help. I would like to see the steps if possible. Thank you!

Solve for t or x. Round off 3 significant decimals
ln(t/t-2)=1
5^(t+1)=6^t
ln9x=1
2=e^(.6t)
1/5=e^(4x)
9ln x = 15
ln 3 + ln x= 1.4
I'll take you through them one at a time if you like, but first show me how you would start Q1.

3. Originally Posted by Jackie10
Hey guys I am new to this website and wanted some help. I would like to see the steps if possible. Thank you!

Solve for t or x. Round off 3 significant decimals
ln(t/t-2)=1
5^(t+1)=6^t
ln9x=1
2=e^(.6t)
1/5=e^(4x)
9ln x = 15
ln 3 + ln x= 1.4
$\ln{\frac{t}{t - 2}} = 1$

$\frac{t}{t - 2} = e^1$

$\frac{t - 2 + 2}{t - 2} = e$

$1 + \frac{2}{t - 2} = e$

$\frac{2}{t - 2} = e - 1$

$\frac{t - 2}{2} = \frac{1}{e - 1}$

$t - 2 = \frac{2}{e - 1}$

$t = \frac{2}{e - 1} + 2$

$t = \frac{2}{e - 1} + \frac{2(e - 1)}{e - 1}$

$t = \frac{2 + 2e - 2}{e - 1}$

$t = \frac{2e}{e - 1}$.

4. Originally Posted by Jackie10
Hey guys I am new to this website and wanted some help. I would like to see the steps if possible. <<<<< we also
Thank you!

Solve for t or x. Round off 3 significant decimals
...
5^(t+1)=6^t
...
1. I assume that you are familiar with the basic laws of powers and logarithms.

2.
$5^{t+1}=6^t$

$5 \cdot 5^t=6^t$

$5=\frac{6^t}{5^t}=\left(\frac65 \right)^t$

$t=\log_{\frac65}(5)=\frac{\ln(5)}{\ln(6)-\ln(5)}$

5. Originally Posted by Jackie10
Hey guys I am new to this website and wanted some help. I would like to see the steps if possible. Thank you!

Solve for t or x. Round off 3 significant decimals
ln(t/t-2)=1
5^(t+1)=6^t
ln9x=1
2=e^(.6t)
1/5=e^(4x)
9ln x = 15
ln 3 + ln x= 1.4
$\ln(9x) = 1$

$9x = e^1 = e\$

$x = \frac{e}{9}$

6. ## Thank you!

So for 2=e^.6t

do i take
ln of both sides

ln2=lne^.6t

then
lne=1

ln2=.6931

.6931=.6t
to get t i divide by .6 to both sides

then i get

.6931/.6

t=1.155

7. Originally Posted by Jackie10
So for 2=e^.6t

do i take
ln of both sides

ln2=lne^.6t

then
lne=1

ln2=.6931

.6931=.6t
to get t i divide by .6 to both sides

then i get

.6931/.6

t=1.155
Correct!!