8^x=60 .............................(1)How do I solve these by hand ? Im able to solve by using logarithms.
8^x=60
3^x=40
using logs I did this x=log 60/log 8 and x=log 40/log 3.
I not sure how to do it by hand.
No, I disagree with you. The answer is x =log(60)/log(8) and you got this result without a calculator. A calculator would give you an approximate answer but you arrived at the exact answer without a calculator. Why do you think that the answer to 8^x = 60 is not x =log(60)/log(8)? If you do think that x =log(60)/log(8) is the correct answer then why do you want to go further?Thank You for taking the time to answer. I arrived at x =log(60)/log(8) which requires a calculator to answer. The questions says to
answer without calculator.
The question says with no calculator estimate the value of x.
a) 8^x=60
b)3^x=40
The exact wording is essential; it is also important to tell us the context of the question. What specific topics were taught before this was asked? Have you been shown any methods for estimating logs?Question 2 is approx 3.35.