1. ## yay logarithms. >:p

ok. i have done these before, but no one can explain 2 me how to solve a fricken logarithmic equation. so if you guys could help me, it would be AMAZING

ok here it is:

Solve each logarithmic equation.

2. Originally Posted by veronica mars
ok. i have done these before, but no one can explain 2 me how to solve a fricken logarithmic equation. so if you guys could help me, it would be AMAZING

ok here it is:

Solve each logarithmic equation.

following the laws of logarithms:

$x = \log_5 \frac 1{625} \implies 5^x = \frac 1{625}$

can you continue?

3. Originally Posted by Jhevon
following the laws of logarithms:

$x = \log_5 \frac 1{625} \implies 5^x = \frac 1{625}$

can you continue?
no that is where i am stuck

4. Originally Posted by veronica mars
no that is where i am stuck
the trick is to express both sides in the same base. do you know what 625 is, if you write it as 5 to some power?

5. Originally Posted by Jhevon
the trick is to express both sides in the same base. do you know what 625 is, if you write it as 5 to some power?
no that is what i can't find. that is where i am stuck. i know that i have to get the same base, but no matter how many times i do it, i cannot figure it out. i have looked in notes, and in examples, and i dont know what could be put to the fifth to equal 625. the only thing i know is what you already said, and that the answer is -4 (i looked in the back of the book)

6. Originally Posted by veronica mars
no that is what i can't find. that is where i am stuck. i know that i have to get the same base, but no matter how many times i do it, i cannot figure it out. i have looked in notes, and in examples, and i dont know what could be put to the fifth to equal 625. the only thing i know is what you already said, and that the answer is -4 (i looked in the back of the book)
how could you not figure it out. just keep multiplying till you get it.

5*5 = 5^2 = 25

5*5*5 = 5^3 = 125

5*5*5*5 = 5^4 = 625 ..........Bingo!

thus we have: $5^x = \frac 1{5^4}$

$\Rightarrow 5^x = 5^{-4}$ .....................since $\frac 1{x^a} = x^{-a}$

equate the powers, since if the bases are the same, the powers must be the same to have equality

thus, $x = -4$

as desired

7. Originally Posted by veronica mars
ok. i have done these before, but no one can explain 2 me how to solve a fricken logarithmic equation. so if you guys could help me, it would be AMAZING

ok here it is:

Solve each logarithmic equation.

$log_{5}\bigg(\frac{1}{625}\bigg)=\log_{5}(5^{-4})=-4$

8. Originally Posted by veronica mars
ok. sorry i didnt know that we werent allowed to not swear and i wasnt sure which catagory my question fell under. this is because i would like to be answered as soon as possible (urgent math help) but if there are other people whose situation is more urgent than mine, i would like to have my question answered in the less urgent area (trigonometry help)

i hope you understand where im coming from
it is ok. it doesn't matter too much. if you post in the wrong category, the mods can move your thread to the right one. don't worry about it, just don't do it again.

and also, this site caters to math of all levels. so kids are often on here. we ask you to refrain from cursing for their sake.

Originally Posted by Mathstud28
$log_{5}\bigg(\frac{1}{625}\bigg)=\log_{5}(5^-4)=-4$