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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: Mulan on May 09, 2010, 08:15:21 pm

Title: indices/ logarithms..help!
Post by: Mulan on May 09, 2010, 08:15:21 pm
how do you solve 5^2x - 5^x+1 = -4   ??
Title: Re: indices/ logarithms..help!
Post by: Mao on May 09, 2010, 08:17:27 pm
Let A = 5^x

A^2 - 5A  + 4 = 0

use quadratic formula. :)
Title: Re: indices/ logarithms..help!
Post by: Mulan on May 09, 2010, 08:21:50 pm
Let A = 5^x

A^2 - 5A  + 5 = 0

use quadratic formula. :)

thats what I did but i got the wrong answer D:
the answers x = 0.86, 0 but i got x = 1,4
i just factorised it to find x, not the quadratic formula. is that wrong?
Title: Re: indices/ logarithms..help!
Post by: Mao on May 09, 2010, 08:26:57 pm
You are almost there, , thus solve and
Title: Re: indices/ logarithms..help!
Post by: Mulan on May 09, 2010, 08:32:14 pm
You are almost there, , thus solve and
omg yea! woopsies.
i forgot that I made 5^x=Y
thanks so much :)
Title: Re: indices/ logarithms..help!
Post by: Mulan on May 10, 2010, 09:47:56 pm
can you help me with another question? xD
solve 5(3^x) - 40 (3^-x)=17 for x
Title: Re: indices/ logarithms..help!
Post by: kamil9876 on May 10, 2010, 09:50:40 pm
multiply both sides by , notice that you get a quadratic similair to the one before.
Title: Re: indices/ logarithms..help!
Post by: Mulan on May 10, 2010, 09:57:17 pm
multiply both sides by , notice that you get a quadratic similair to the one before.
y do you multiply both sides by 3^x?
Title: Re: indices/ logarithms..help!
Post by: m@tty on May 10, 2010, 10:06:40 pm
So that
you get a quadratic similair to the one before.

It is much easier to solve.





. where (which holds for all real numbers.)

Then solve as a quadratic in as before.
Title: Re: indices/ logarithms..help!
Post by: Mulan on May 10, 2010, 10:12:42 pm
So that
you get a quadratic similair to the one before.

It is much easier to solve.





. where (which holds for all real numbers.)

Then solve as a quadratic in as before.

ohhhh thanks you guys :) really helped a lot