Solving Exponential Equations (lacking a common base)
31^d=38

d = log 38/log31

d = 1.06

Step-by-step explanation:

31 ^ d = 38

Take log of both sides since the exponential equation have different base (always)

d log 31 = log 38

d = log 38 / log 31

d = 1.58 / 1.491

d = 1.06.

We can actually check to see if this is correct.

Substituting d = 1.06

31^ 1.06 = 38.092

(You see, that's approximately correct)

Keep learning, maths is fun!

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490