Soru:1
- [tex]10^{x} =20[/tex]
- [tex]2^{x+1} .5^{x-1}=?[/tex]
[tex]10^{x} =2^{x} .5^{x} =20[/tex]
[tex]2^{x+1} .5^{x-1}=2^{x}.2.5^{x}.\frac{1}{5}[/tex]
[tex]20.2.\frac{1}{5} =8[/tex]
Soru:2
- [tex]2^{x} +2^{x} +2^{x} +2^{x} =4^{x} .4^{x}[/tex]
- x=?
[tex]4.2^{x} =16^{x} \\2^{x+2} =2^{4x} \\x+2=4x\\2=4x-x\\2=3x\\\frac{2}{3} =x[/tex]
Soru:3
- [tex]2.3^{x} +5.3^{x}-3.3^{x}=108\\[/tex]
- x=?
[tex]3^{x}.(2+5-3)=108\\3^{x}.4=108\\3^{x}=27\\3^{x}=3^{3}\\x=3[/tex]
Soru:5
- [tex]6.2^{x}+2.2^{x} -5.2^{x} =48[/tex]
- x=?
[tex]2^{x}.(6+2-5)=48\\2^{x}.3=48\\2^{x}=16\\2^{x} =2^{4}\\x=4[/tex]
Soru:6
- [tex](\frac{4}{25}) ^{x+1}=\frac{125}{8}[/tex]
- x=?
[tex](\frac{2^{2}}{5^{2} })^{x+1}=\frac{5^{3} }{2^{3} } \\\\(\frac{2}{5})^{2x+2}=(\frac{5}{2})^{3} \\\\2x+2=-3\\\\2x=-3-2\\\\2x=-5\\\\x=\frac{-5}{2}[/tex]
Soru:7
- [tex]10^{x+2} =5^{x+1}[/tex]
- [tex]2^{x+2}=?[/tex]
[tex]5^{x+2} .2^{x+2} =5^{x+1} \\\\25.5^{x} .2^{x+2}=5.5^{x}\\\\5.2^{x+2}=1\\\\2^{x+2}=\frac{1}{5}[/tex]
