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The solution of the equation (log)7(log)...

The solution of the equation `(log)_7(log)_5(sqrt(x+5)+sqrt(x)=0` is...

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`log_7 (log_5 (sqrt(x+5)+sqrtx))=0`
`log_5(sqrt(x+5)+sqrtx))=7^0=1`
`sqrt(x+5)+sqrtx=5^1=5`
Squaring both sides
`x+5+x+2sqrtxsqrt(x+5)=25`
`2sqrtxsqrt(x+5)=25-5-2x`
`2sqrtxsqrt(x+5)=20-2x=2(10-x)`
`sqrtxsqrt(x+5)=10-x`
...
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CENGAGE ENGLISH-LOGARITHM-All Questions
  1. Find the smallest integral value of x satisfying (x-2)^(x^2-6x+8))&gt...

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  2. The least value of the expression 2(log)(10)x-(log)x(0.01)dot for x &...

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  3. The solution of the equation (log)7(log)5(sqrt(x+5)+sqrt(x)=0 is...

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  4. Let (x0, y0) be the solution of the following equations: (2x)^(1n2)=(3...

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  5. If In(a+c),ln(a-c),ln(a-2b+c) are in AdotPdot, then a , b , c ,a r ...

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  6. Prove that number (log)2 7 is an irrational number.

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  7. Which of the following numbers are positive/negative? (log)2 7 (ii) (...

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  8. If (log)3 2,(log)3(2^x-5)a n d(log)3(2^x-7/2) are in arithmetic progre...

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  9. Solve x^((log)y x)=2a n dy^((log)x y)=16

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  10. Solve (log)(2x)2+(log)4 2x=-3//2.

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  11. If ageqb >1, then find the largest possible value of the expression (l...

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  12. Solve : 3^((log9 x))xx2 = 3sqrt(3)

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  13. Solve the inequality sqrt((log)2((2x-3)/(x-1)))<1

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  14. Find the number of solutions of equation 2^x+3^x+4^x-5^x=0

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  15. If y=a^(1/(1-(log)a x)) and z=a^(1/(1-(log)a y)),then prove that x=a^...

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  16. Solve (log)x2(log)(2x)2=(log)(4x)2.

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  17. Let a , b , c , d be positive integers such that (log)a b=3/2a n d(log...

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  18. Solve sqrt("log"(-x))=logsqrt("x"^2) (base is 10).

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  19. If (log)3{5+4(log)3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (...

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  20. If (log)(10)[1/(2^x+x-1)]=x[(log)(10)5-1] , then x= 4 (b) 3 (c) 2 ...

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