Phillip is using logarithms to solve the equation 63x = 18. Which of the following equations would be equivalent to his original expression?

6 log 3x = log 18

3 log 6 = x log 18

x log 3 = 6 log 18

3x log 6 = log 18

Question

Phillip is using logarithms to solve the equation 63x = 18. Which of the following equations would be equivalent to his original expression?

 6 log 3x = log 18

 3 log 6 = x log 18

 x log 3 = 6 log 18

 3x log 6 = log 18

zepdrix · Answer

I don't understand the original expression.

Is it supposed to be 6(3^x) = 18 ?

zepdrix · Answer

Or (63)^x = 18 maybe?

anonymous · Answer

the 3 x is an exponent

zepdrix · Answer

6^(3x) = 18

We can take the log of each side:

log[ 6^(3x) ] = log 18

zepdrix · Answer

There is a rule of logs that allows us to deal with powers.

log[ a^b ] = b*log a

zepdrix · Answer

See how we can use that rule to move the 3x?

anonymous · Answer

yes but i dont get it

zepdrix · Answer

So using the rule,

log[ 6^(3x) ] = log 18

allows us to bring our 3x down in front of the log as a coefficient

3x log 6 = log 18