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JayDS
 3 years ago
Find the equation of the inverse of the following.
JayDS
 3 years ago
Find the equation of the inverse of the following.

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Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1the inverse is just if you put in an x and get a y the inverse is like putting in the y and getting the same x you put in the first part.

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1what you can do is switch your x's and y's then just solve for y.

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1\[y=3^{x}\] \[x=3^{y}\] \[\log _{10}x = \log _{10}3^{y}\] \[\log _{10} x = ylog _{10}3\] \[y=\frac{\log _{10}x}{\log _{10}3}\] y=x/3?

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1I have answers but I want to know what I did wrong, because it seems right to me.

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1i think you need to keep the logs or put e^y

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1you can only take away the logs like you did if y had one on that side

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1i think it can be rewrote as y=ln(x3) but i'm a little rusty with logarithms

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1but there is log10 on both sides, so I can cancel it out? and ok... I'm still confused sorry.

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1when you moved the y over to the other sice you had y=log(x)/log(3) y doesn't have a log

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1if it was log(y)=log(x)/log(3) you could cancel them out

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1really? hmmm, confusing but I know what you mean.

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1yeah i get confused too when you start using logs

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1if you have the answer try to work it backwards to get the first question and try to tie the two to gether with what your sure of.

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1the answer is \[\log _{3}x for x>0\] can you help me out? I don't understand how they got it.

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1\[\log_{a}y=x \] is \[a^{x}=y\]

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1from log10(x)=ylog10(3) can you show me the rest of the steps?

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1so we can rewriteyour first one as as\[\log_{3} x=y\]

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1after you switch the x and y I believe?

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1sorry i'm trying to remember this as we go

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1no that is just rewriting it then we swith and solve for x

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1all i did was change the exponent to a log

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1\[y=3^{x}\] \[\log _{3}y=x\]

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1I think you got confused with the x and y, you just got them in the wrong position.

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1then we can switch the x & y from there.

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1it's hard to do math on these boards lol

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1yeh I know haha, especially trying to write the equation takes years.

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1i think i have it let me check with my calculator

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1ok lol i can't figure out how to do it on my calculator but i think it's right, so all we are doing is changing the question into a log of the same equasion then when we swap x and y we already have the answer

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1by the rules of logarithms we have loga^b=c is the same as a^c=b

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1ok, and it turns out to be\[y=\log _{3}x\] right?

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1so taking your problem y=3^x and putting it in log form we get log3^y=x then we swap y and x to get log3^x=y is that right?

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1so let's try the second one

Jusaquikie
 3 years ago
Best ResponseYou've already chosen the best response.1y=5^x is log5^y=x so swap is log5^x=y

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1yep but the answer only says 5^x for some reason.

JayDS
 3 years ago
Best ResponseYou've already chosen the best response.1confusing, I'll just have to ask my teacher. I'm just doing it advanced anyway.
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