Please help, im so confused.
how would you solve:
2log(subscript6)(4) - (1/3)log(sub6)(8) = log(sub6)(x)
I did that for you already.
thanks
Given that given that x square + y square equals to 5 x y show that 2log x + y over square 7 equal to log x + log y
To solve the equation 2log₆(4) - (1/3)log₆(8) = log₆(x), follow these steps:
Step 1: Simplify the logarithmic expressions
Using the properties of logarithms, we can simplify the equation.
2log₆(4) can be rewritten as log₆(4²), which equals log₆(16).
Similarly, (1/3)log₆(8) can be written as log₆(8^(1/3)), which equals log₆(2).
So, the equation becomes log₆(16) - log₆(2) = log₆(x).
Step 2: Combine the logarithms
Using the logarithmic property logₐ(p) - logₐ(q) = logₐ(p/q), we can combine the left side of the equation.
Therefore, log₆(16) - log₆(2) can be simplified to log₆(16/2) = log₆(8) = log₆(x).
Step 3: Solve for x
Now that we have the equation log₆(8) = log₆(x), we can conclude that x = 8.
So, the solution to the equation 2log₆(4) - (1/3)log₆(8) = log₆(x) is x = 8.