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CHHAYA PUBLICATION-LAWS OF INDICES-Short Answer Type Questions
- If a=2^(1/3)-2^(-1/3) show that 2a^(3)+6a-3=0
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- If x=2+2^(2/3)+2^(1/3) show that x^(3)-6x^(2)+6x-2=0
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- If x^(1/a)=y^(1/b)=z^(1/c ) and xyz =1 show that a+b+c=0
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- If a^(1/3)+b^(1/3)+c^(1/3)=0 show that (a+b+c)^(3)=27 abc
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- If x^(a)=y^(b)=(xy)^(c ) prove that ab=c(a+b)
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- If x^(a)=c^(b) and x^(c )=c^(a) show that a^(2)=bc
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- If x^(y)=y^(x) show that (x/y)^(x/y)=x^((x)/(y)-1) if further x=2y t...
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- If p^(a)=q^(b)=r^(c ) and pqr=1 show that ab+bc+ca=0
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- If 2^(x)=3^(y)=12^(z) show that xy=z(x+2y)
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- If (a-(1)/(a))^(2)=3 show that a^(6)+(1)/(a^(6))=110
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- If x^(3)=y^(4) prove that (x/y)^(4/3)+(y/x)^(3/4)=x^(1/3)+y^(-1/4)
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- If a^(x)=b,b^(y)=c,c^(z)=a show that xyz =1 (a,b,c positive num...
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- If (x^(n^3))^(n)=(x^(3^n))^(3) show that root(n+1)(n^(4))=3
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- If x^(p^q)=(x^sqrt(p))^(q) find p in terms of q
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- If (56)^(a)=(5.6)^(b)=10^(c ) show that (1)/(a)=(1)/(b)+(1)/(c )
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- 6^(2x+4)=3^(3x).2^(x+8)
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- 4^(x)-3.2^(x+2)+2^(5)=0
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- 3^(2x)+9=10.3^(x)
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- 3^(x)+3^(y)=4,3^(-x)+3^(-y)=4/3
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- 8^(x).4^(y)=128,9^(x+y)=(27)^(xy)
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