When unknown is in a rational exponent?

[JaZoN_XD]

Hi guys, I tried searching everywhere for a guide to teach me but I couldn't find anything. What do I do if the x is in a rational exponent like this? 2=2^((1970-x)/2)    ??????????? Thanks for anyone who helps. Thanks LTT math kids

[Clear17Mud]

you change it to a log.

 

EDIT: you asked what you do not how you do it

[TheKDub]

Hi guys, I tried searching everywhere for a guide to teach me but I couldn't find anything. What do I do if the x is in a rational exponent like this? 2=2^((1970-x)/2)    ??????????? Thanks for anyone who helps. Thanks LTT math kids

 

log2 = log2((1970-X)/2)

 

Which is the same as

log2 = ((1970-X)/2)log2

so divide both sides by log2 to get

(log2)/(log2) = (1970-x)/2

1 = (1970-X)/2

Multiply both sides by 2

2 = 1970-X

add x to both sides, subtract 2 from both sides.

X = 1968.

 

 

(Log is short for Logarithm)

[zlolslavez]

here's my horrid paint drawing for the basic of it (I don't explain how to solve the log, but log2(2) * 2 = 2

also try this website http://www.mathpapa.com/algebra-calculator.html

[ryanmmax]

you change it to a log.

 

you asked what you do not who you

 

Specifically you use the properties of log in this case Log(B^X)=X*Log('B') 

 

2=2^((1970-x)/2)

log(2)=log(2^((1970-x)/2))=(1970-x)/2*log(2)

 

1=(1970-x)/2

2=1970-x

1968=x

 

 

*Edit*  they beat me to it.... Well at least we all got the same answer....

[JaZoN_XD]

log2 = log2((1970-X)/2)

 

Which is the same as

log2 = ((1970-X)/2)log2

so divide both sides by log2 to get

(log2)/(log2) = (1970-x)/2

1 = (1970-X)/2

Multiply both sides by 2

2 = 1970-X

add x to both sides, subtract 2 from both sides.

X = 1968.

 

 

(Log is short for Logarithm)

 

 

here's my horrid paint drawing for the basic of it (I don't explain how to solve the log, but log2(2) * 2 = 2

also try this website http://www.mathpapa.com/algebra-calculator.html

 

 

Specifically you use the properties of log in this case Log(B^X)=X*Log('B') 

 

2=2^((1970-x)/2)

log(2)=log(2^((1970-x)/2))=(1970-x)/2*log(2)

 

1=(1970-x)/2

2=1970-x

1968=x

 

 

*Edit*  they beat me to it.... Well at least we all got the same answer....

Thank you guys SOOO much! Thanks for all the help! LTT *almost* never disappoints! 

[JaZoN_XD]

Hey does anyone still have time for another? This time it's similar but I'm still stuck like a moron.

 

4=r^(2011-k)+2

 

2=r^(1985-k)+2

 

I tried isolating one of them but i end up getting a bunch of logs and things don't cancel out and i'm panicking... 

 

@ryanmmax mind if I tag you?