I can't seem to get the answer to this; the answer key says log(base 8)6
Write as a single logarithm
log(base 8)42log(base 8)3 - log(base 8) 6
I'm hoping the key is wrong :)
Thank you for your help!
log8(4)*2log8(3)-log8(6)
take antilog...
antilog8 (4*9/6)= antilog8(6)
take log8= log8(6)
To write the given expression as a single logarithm, we can use the following properties of logarithms:
1. Product Rule: log(base a)(b) + log(base a)(c) = log(base a)(b * c)
2. Quotient Rule: log(base a)(b) - log(base a)(c) = log(base a)(b / c)
Using these properties, let's simplify the expression step by step:
Step 1:
We have: log(base 8)(42) * log(base 8)(3) - log(base 8)(6)
Step 2:
Apply the Product Rule to the first two terms:
log(base 8)(42 * 3) - log(base 8)(6)
Step 3:
Simplify the logarithmic expression in the first term:
log(base 8)(126) - log(base 8)(6)
Step 4:
Apply the Quotient Rule to subtract the second term:
log(base 8)(126 / 6)
Step 5:
Simplify the expression inside the logarithm:
log(base 8)(21)
Therefore, the simplified expression is log(base 8)(21).
I hope this helps! If you still have any doubts, feel free to ask.