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Solve: (log)2(4.3^x-6)-(log)2(9^x-6)=1....

Solve: `(log)_2(4.3^x-6)-(log)_2(9^x-6)=1.`

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`log_2[(4*3^x-6)/(3^(2x)-6)]=1`
`(4*t-6)/(t^2-6)=2`
`4t-6=2t^2-12`
`2t^2-4t-6=0`
`t^2-3t+t-3=0`
`t(t-3)+1(t-3)=0`
`(t-3)(t+1)=0`
`t=3,-1`
...
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CENGAGE-LOGARITHM-Solved Examples And Exercises
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  5. Which of the following pairs of expression are defined for the same se...

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  6. Solve (log)2(3x-2)=(log)(1/2)x

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  7. Solve log(-x)=2log(x+1)dot

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  8. Solve: (log)2(4.3^x-6)-(log)2(9^x-6)=1.

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  9. Solve 2^(x+2)27^(x//(x-1))=9

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  11. If (log)(12)27=a , then find (log)6 16 interms of a

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  12. If y^2=x z and a^x=b^y=c^z , then prove that (log)ab=(log)bc

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  13. Simplify: 1/(1+(log)a b c)+1/(1+(log)b c a)+1/(1+(log)c a b)

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  14. If a^x=b ,b^y=c ,c^z=a , then find the value of x y zdot

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  15. Find the value of ((log)3 4)((log)4 5)((log)5 6)((log)6 7)((log)7 8)((...

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  16. y=2^(1/((log)x4), then find x in terms of y.

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  17. If n >1,t h e np rov et h a t 1/((log)2n)+1/((log)3n)++1/((log)(53)n)...

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  18. What is logarithm of 32^5sqrt(4) to the base 2sqrt(2)?

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  19. Which is greater: x=(log)3 5ory=(log)(17)25 ?

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  20. The product of roots of the equation (log8(8/x^2))/((log8x)^2)=3 is 1 ...

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