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Homework Statement
[tex] log_4(5-x)-log_4(3-x) = 2 [/tex]
The Attempt at a Solution
[tex] log_4(5-x)-log_4(3-x) = 2 [/tex]
[tex] log_4\frac{3-x}{5-x} = 2 [/tex]
where do I go from here?
Cyosis said:What do you know about [tex]a^\log_a x[/tex]?
[itex]log_a(b)= c[/itex] is equivalent to [itex]b= a^c[/itex]. Here, a= 4, b= (3-x)/(5- x), and c= 2.tweety1234 said:Homework Statement
[tex] log_4(5-x)-log_4(3-x) = 2 [/tex]
The Attempt at a Solution
[tex] log_4(5-x)-log_4(3-x) = 2 [/tex]
[tex] log_4\frac{3-x}{5-x} = 2 [/tex]
where do I go from here?
HallsofIvy said:[itex]log_a(b)= c[/itex] is equivalent to [itex]b= a^c[/itex]. Here, a= 4, b= (3-x)/(5- x), and c= 2.
The equation represents a logarithmic function with base 4, where the difference between the inputs of the two logarithms is equal to 2.
To solve this equation, you can use the quotient property of logarithms, which states that log(a/b) = log(a) - log(b). You can also use algebraic manipulation to isolate the variable and solve for it.
The steps to solving this equation are:
Yes, you can use a calculator to solve this equation. However, it is important to make sure your calculator is set to the correct base, in this case base 4, and to use parentheses to group the terms correctly.
Yes, there is a shortcut known as the logarithmic identities, which states that log(a) - log(b) = log(a/b) and log(a) + log(b) = log(ab). These identities can help simplify the equation and make it easier to solve.