SOLUTION: given that log27(base a)+log4(base b)=5 and log27(base a)-log4(base b)=1 without using tables,find the values of a and b
Algebra.Com
Question 413995: given that log27(base a)+log4(base b)=5 and log27(base a)-log4(base b)=1 without using tables,find the values of a and b
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let )
Let )
Then
Using elimination
Hence:
\ =\ 3\ \Leftrightarrow\ a^3\ =\ 27\ \Rightarrow\ a\ =\ 3)
\ =\ 2\ \Leftrightarrow\ b^2\ =\ 4\ \Rightarrow\ b\ =\ \pm2)
But the base of a logarithm function is restricted to the positive reals, hence
John
My calculator said it, I believe it, that settles it
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