1. ## Logarithm qsn :D

Hi all!

Just wondering whether i could get some help solving this question for "t"? Do you have to put log10 on each side? Step by step if possible would be greatly appreciated.

20(10^0.1t) = 25(10^0.05t)

Cheers

2. I would divide both sides by 20, then divide both sides by $\displaystyle 10^{0.05t}$.
You can use index laws to simplify your exponents.

Then I would take a log of both sides.

3. Originally Posted by steph_r
Hi all!

Just wondering whether i could get some help solving this question for "t"? Do you have to put log10 on each side? Step by step if possible would be greatly appreciated.

20(10^0.1t) = 25(10^0.05t)

Cheers
$\displaystyle 20\left(10^{0.1t}\right) = 25\left(10^{0.05t}\right)$

$\displaystyle \frac{\left(10^{0.1t}\right)}{\left(10^{0.05t}\rig ht)} = \frac{25}{20}$

$\displaystyle 10^{0.1t - 0.05t} = \frac{5}{4}$

$\displaystyle 10^{0.05t} = \frac{5}{4}$

$\displaystyle 0.05t = \log_{10}{\frac{5}{4}}$

$\displaystyle t = 20\log_{10}{\frac{5}{4}}$