4.5.2 Indices and Logarithms, Short Questions (Question 5 – 7)


Question 5
Solve the equation,  log 2 4 x = 1 log 4 x

Solution:
log 2 4 x = 1 log 4 x log 2 4 x = 1 log 2 x log 2 4 log 2 4 x = 1 log 2 x 2 2 log 2 4 x = 2 log 2 x log 2 16 x 2 = log 2 4 log 2 x log 2 16 x 2 = log 2 4 x 16 x 2 = 4 x x 3 = 4 16 = 1 4 x = ( 1 4 ) 1 3 = 0.62996



Question 6
Solve the equation,  log 4 x = 25 log x 4

Solution:
log 4 x = 25 log x 4 1 log x 4 = 25 log x 4 1 25 = ( log x 4 ) 2 log x 4 = ± 1 5 log x 4 = 1 5    or    log x 4 = 1 5 4 = x 1 5     4 = x 1 5 x = 4 5 4 = 1 x 1 5 x = 1024   x 1 5 = 1 4     x = 1 1024


Question 7
Solve the equation,  2 log x 5 + log 5 x = lg 1000

Solution:
2 log x 5 + log 5 x = lg 1000 2. 1 log 5 x + log 5 x = 3 × ( log 5 x ) 2 + ( log 5 x ) 2 = 3 log 5 x ( log 5 x ) 2 3 log 5 x + 2 = 0 ( log 5 x 2 ) ( log 5 x 1 ) = 0 log 5 x = 2   or   log 5 x = 1 x = 5 2   x = 5 x = 25

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