# Logarithmic Functions

• Nov 11th 2009, 05:59 PM
yzobel
Logarithmic Functions
1) ln(2t+1)=2-lnt Solve for t.
I just want to know whether I need to move lnt to the left side in order to solve the equation or can I just leave the equation as is and multiply both sides by e.

2) This problem has been bothering me for a while.
Differentiate y=10^tan(theta)

I tried to solving it earlier but I got stuck:
log10y=tan(theta)
So now can I use implicit differentiation?

Thank you!
• Nov 11th 2009, 06:09 PM
bigwave
now or later
you will have all the terms with t to one side eventually...
might as well do it early on....doesn't have to be first step tho..
• Nov 11th 2009, 06:10 PM
tonio
Quote:

Originally Posted by yzobel
1) ln(2t+1)=2-lnt Solve for t.
I just want to know whether I need to move lnt to the left side in order to solve the equation or can I just leave the equation as is and multiply both sides by e.

You don't multiply by e: you APPLY e at both sides. But first move ln t to the left side:

$\ln((2t+1)t)=2\Longrightarrow 2t^2+t=e^2...$

2) This problem has been bothering me for a while.
Differentiate y=10^tan(theta)

I tried to solving it earlier but I got stuck:
log10y=tan(theta)
So now can I use implicit differentiation?

Indeed: $\frac{1}{y}dy=\frac{1}{\cos^2\theta}d\theta$ and etc.

Tonio

Thank you!

.