Question

$log_{12}(18) = a \\ so \: what \: is \: the \: value \: of \: \\ log_{24}(16)$
pls anyone answer this question

Answer 1

I’ll denote logx to the base y by 'log_y (x)'.

Now, given, log_18 (12) = a ….(1)

We have to find the value of,

= log_24 (16)

= log_18 (16/) / log_18 (24)

= log_18 (2^4) / log_18 (8×3)

= 4log_18 (2) / {log_18 (8) + log_18 (3)}

= 4log_18 (2) / {log_18 (2^3) + log_18 (3)}

= 4log_18 (2) / {3log_18 (2) + log_18 (3)}

= 4/{3+log_18 (3)/log_18 (2)}

= 4/{3+log_2 (3)}

= 4/(3+p) ; where, p = log_2 (3) ….(2)

Now, from (1), we have,

log_2 (12) / log_2 (18) = a

=> log_2 (3×4) / log_2 (2×9) = a

=> log_2 (3×2^2) / log_2 (2×3^2) = a

=> {log_2 (3) + 2log_2 (2)} / {log_2 (2) + 2log_2 (3)} = a

=> (p+2×1)/(1+2p) = a

=> p+2 = a+2ap

=> p = (a-2)/(1–2a)

Therefore, from (2), we get,

log_18 (16) / log_18 (24) = 4/{3+(a-2)/(1–2a)}

= 4(1–2a)/(1–5a) . (Ans)

Hope, it'll help..!!

Answer 2

Answer:

l don't know this question ❓❓