Question

If the base is 2√3, find the value of log169

Answer 1

Answer:

chapati hindustan gamer

Answer 2

Given : base is 2√3,

To  find :   the value of log 169

Solution:

log 169  base is 2√3,

$\log _{2 \sqrt{3}} 169$

logₐb = log b / log a

= log 169 / log 2√3

=  log 13² / log 2√3

= 2 log 13 / log 2√3

log ab = log a + log b

log 2√3 = log2  + log √3

log aⁿ = n log a

=> log 2√3 = log2  +(1/2) log 3

log 13 = 1.114

log2 = 0.3010

log 3 = 0.4771

= 2(1.114)/ ( 0.3010 + (1/2)0.4771)

= 2.228/(0.53955)

= 4.1294

$\log _{2 \sqrt{3}} 169$  = 4.1294

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