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Help on exponential equations?
These are the equations that go such as
7^m = 7^n
so m=n
1) (2/3)^4x = (9/4)^x+6
2) 49^x = √(7)
3) 6^x-1 = 10^x
To solve these the bases must be equal, help is greatly appreciated. :)
1 Answer
- JuanLv 68 years agoFavorite Answer
1) (2/3)^4x = (9/4)^x+6
Do you mean (2/3)^4x = (9/4)^(x+6)
(2/3)^4x = (2/3)^[(-2)(x+6)]
(2/3)^4x = (2/3)^(-2x-12)
4x=-2x-12
6x=-12; x=-2
2) 49^x = √(7)
49^x=7^(1/2)
(7^2)^x=7^(1/2)
7^(2x)=7^(1/2)
x=1/4
3) 6^x-1 = 10^x
do you mean 6^(x -1) = 10^x
use the formul; a^x=e^(x*lna)
e^[(x-1)ln6]=e^(x*ln10)
x*ln6-ln6=x*ln10
-ln6=x*ln10-x*ln6
-ln6=x(ln10-ln6)
ln6=x(ln6-ln10)
ln6/(ln6-ln10)=x
