HSC Arts कक्षा ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Solve log₄ 2^8x = 2^log₂8 

If a² + b² = 7ab, show that `log  ("a" + "b")/3 = 1/2(log"a" + log "b")`

Prove `log  "a"^2/"bc" + log  "b"^2/"ca" + log  "c"^2/"ab"` = 0

Prove that `log 2 + 16log  16/15 + 12log  25/24 + 7log  81/80` = 1

Prove that log_a² a + log_b² b + log_c² c = `1/8`

Prove log a + log a² + log a³ + · · · + log aⁿ = `("n"("n" + 1))/2 log "a"`

If `log x/(y - z) = logy/(z - x) = logz/(x - y)`, then prove that xyz = 1

Solve `log_2 x − 3 log_(1/2) x` = 6

Solve log_{5 – x} (x² – 6x + 65) = 2

Choose the correct alternative:
The value of `log_(sqrt(5))` 512 is

Choose the correct alternative:
The value of `log_3  1/81` is 

Choose the correct alternative:
If `log_(sqrt(x)` 0.25 = 4, then the value of x is

Choose the correct alternative:
The value of log_ab  log_bc  log_ca is

Choose the correct alternative:
If 3 is the logarithm of 343, then the base is

Choose the correct alternative:
The value of log₃ 11 . log₁₁ 13 . log₁₃ 15 . log₁₅ 27 . log₂₇ 81 is