# Math Help - Solving Exponential Equations

1. ## Solving Exponential Equations

Question is in the link. I just can't figure these 2 out.
Thanks a lot....again!

http://img9.imageshack.us/img9/7561/60225025.jpg (that exponent on the second equation is a -t)

Auger

2. Originally Posted by Auger
Question is in the link. I just can't figure these 2 out.
Thanks a lot....again!

http://img9.imageshack.us/img9/7561/60225025.jpg (that exponent on the second equation is a -t)

Auger
$(\frac{1}{32})^{4x} = 1024$

All these numbers are powers of two so it can be expressed as:

$\frac{1}{2^{20x}} = 2^{-20x} = 2^{10}$

If the bases are equal then the exponents must be equal: $-20x = 10$. Should be clear that $x = -0.5$

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$\frac{20}{3+4e^{-t}} = 5$

Take the reciprocal of both sides and then multiply by 20

$3+4e^{-t} = 4$

Take 3 and then divide by 4:

$e^{-t} = \frac{1}{4}$

$-t = -ln(4) = -2ln(2)$

$t = 2\,ln2$

3. sorry i don't understand how you got to the second step. I have not learnt this. Could you explain?

thanks