logb 2 SolutionSolution a 1296 can be written as 2 x2x2x2 x

Solution

Solution:

(a) 1296 can be written as = 2 x2x2x2 x3x3x3x3

= 2⁴ x 3⁴

log_b1296 = log₂ (2⁴x3⁴)

=    log₂ 2⁴ +  log₂ 3^{4 ....} log(AB) = logA + logB

= 4 log₂2 + 4 log₂3 ... Log AB = B xlogA

= 4x + 4y

(b)

324 = 2²x3⁴

= log_b(2²x3⁴)

= log_b2² + log₂3⁴

= 2 log_b2 + 4 log₂3

= 2x +4y

(c) log_b (16/3)

= log_b16 - log_b 3

= log_b2⁴ - log_b3

= 4x -y

(d) log_b81/log_b8 = log_b3⁴/log_b2³

= 4y/3x

Answer