Question

Logarithms: Solve
6(10^2x) + 10^x - 2 =0

Answer 1

Consider that 10^2x is really like saying (10^x) squared, or:\[(10^x)^2\]Now, rewrite the original problem by using a substitution of \[y=10^x\]Using that substitution, your original equation can be rewritten as\[6y^2+y-2=0\]which can be solved in a variety of manners (quadratic, factoring, etc). Just keep in mind when you do solve that the answer you're getting is y, not the original problem. Once you have y, replace y with the original 10^x and complete the problem.

Answer 2

okay thank you :)

Answer 3

yeah and unfortunately the solution is very ugly because this one does not factor over integers

Answer 4

6y^2+4y-3y-2=0

Answer 5

postive solution is
\[\frac{-5+\sqrt{37}}{6}\]so answer is
\[\log(\frac{-5+\sqrt{37}}{6})\]

Answer 6

2y(3y+2)-(3y+2)=0
(2y-1)(3y+2)=0

Answer 7

oh heavens you are right. i sovled
\[+y^2+10y-2=0\] like a dope

Answer 8

y=1/2
y=-2/3
but u need solve for x
remember y=10^x

Answer 9

stop showing off your "splitting the middle term"!

Answer 10

10^x=1/2
10^x=-2/3
satellite will tell u the rest

Answer 11

satellite is beet red

Answer 12

discard negative answer and write
\[\log(\frac{1}{2})\]

Answer 13

and dont forget you can't have log of a negative

Answer 14

oh you already said it

Answer 15

lol

Answer 16

i must be tired. jealous because polpak gets to be green and i don'

Answer 17

satellite amistre is also green did you know?