Question

Logarithms

Please do not answer with a link, not only can I not access it (nor would I be comfortable doing so) but the answer will be immediately deleted.

Answer 1

`\huge\boxed{\sf -2.280}`

Explanation:

Finding value of log₃(4/49):

`\displaystyle = log_(3)(4)/(49) \\\\= log_(3) ((4)/(7^2) )\\\\\underline{Using \ log \ rule \ :} \ log( (a)/(b) )= log \ a - log \ b \\\\= log_(3)4 - log_(3)7^2\\\\\underline{Using \ log \ rule \ : } \ log \ a ^m = m \ log \ a \\\\= log_(3)4 - 2(log_(3)7)\\\\`

Given that:

log₃4 ≈ 1.262, log₃7 ≈ 1.771

Put the values in the above expression

`= 1.262-2(1.771)\\\\= 1.262 - 3.542\\\\= \bold{-2.280}\\\\\rule[225]{225}{2}`