Solve 4^(x – 2) = 3 using common logarithms.

Question

anonymous · Answer

$$b^x=A\iff x=\frac{\log(A)}{\log(b)}$$

anonymous · Answer

$$4^{x-2}=3\iff x-2=\frac{\log(3)}{\log(4)}$$

anonymous · Answer

"solve using common logs"??!! it makes no difference what log you use

anonymous · Answer

honestly i dont understand how to do it at all :/

anonymous · Answer

@satellite73 so wouldnt the log cancel out and it be 3/4??? or is that completely wrong?

anonymous · Answer

yes, that is completely wrong
the log is not a number, it is a function

anonymous · Answer

you should have the button on your calculator to compute $\log(3)$

anonymous · Answer

so i would do log 3/log 4?

anonymous · Answer

lets do a simpler example 
$$2^x=10$$ solve in one step using a calculator 
$$x=\frac{\log(10)}{\log(2)}$$

anonymous · Answer

3.321928095

anonymous · Answer

x is the log of the total divided by the log of the base

anonymous · Answer

so for the original problem would it be....79248125?

anonymous · Answer

in your case you have 
$$x-2=\frac{\log(3)}{\log(4)}$$ so 
$$x=\frac{\log(3)}{\log(4)}+2$$

anonymous · Answer

so 2.792?

anonymous · Answer

i get this http://www.wolframalpha.com/input/?i=log(3)%2Flog(4)%2B

anonymous · Answer

alright, thank you so so much :DDD

anonymous · Answer

yw

anonymous · Answer

can i ask you one more?

anonymous · Answer

sure

anonymous · Answer

A scientist has 86 grams of a radioactive substance that decays at an exponential rate. Asuming k = –0.4, how many grams of radioactive substance remain after 10 days?

anonymous · Answer

$$86\times e^{-.4\times 10}=86\times e^{-4}$$ and a calculator

anonymous · Answer

how did you just do that?!

anonymous · Answer

i am assuming the rate is in days

anonymous · Answer

yeah, thats what the problem was, i just copied and pasted it.

anonymous · Answer

$$A_0e^{kt}$$ with $A_0=86$ and $k=-0.4$

anonymous · Answer

and $t=10$

anonymous · Answer

so would it be..195.533

anonymous · Answer

no

anonymous · Answer

then what would it be??

anonymous · Answer

it is decaying so there must be less, not more

anonymous · Answer

http://www.wolframalpha.com/input/?i=86e^-4

anonymous · Answer

so would i do negative 4 then?

anonymous · Answer

would i subtract that from the 86 then?

anonymous · Answer

no that is the answer
compute it with a calculator

anonymous · Answer

the answer is 
$$86\times e^{-4}$$ but you need a calculator to compute that number, or use the link i sent

anonymous · Answer

yeah i got it, thank you so much!

anonymous · Answer

yw