Question

log( b)√8= 16÷3 then b=​

Answer 1

Answer:

This question can be solved by 3 basic logarithmic rules.

1.logb(m^n) = n · logb(m)

2. logb^n(m) = 1/n.logb(m)

3 . logb(x) = c, then x = b^c

sqrt(8) can be written as 2^3/2.

Now plugging it in our question, we get

log2^3/2(x) = 1/(3/2)log2(x)

=> 2/3 log2 (x) = 10/3

=> log2(x) = (10/3)*(3/2)

=> log2(x) = 5

=> x = 2^5

=> x = 32.

Hence, the answer. :)