find the value of?

Question

lim (6^x - 7^x)/ (4x)
x->0

Answer 1

amit is right but still if you haven't studied l'hopital that might be hard to comprehend
we can rewrite the limit like this
lim 1/4 (6^x-1)/x - (7^x-1)/x
x->0

we apply the limit

lim (a^x-1)/x= ln(a) with a>0
x->0

1/4 (ln6-ln7)

1/4 (ln(6/7))

Answer 2

Use L'hospital's rule:

lim (x->0) (6^x - 7^x)/(4x) =
= lim (x->0) (6^x ln6 - 7^x ln7)/4 =
= (ln 6 - ln 7)/4