To solve this logarithmic equation, we first need to use the property of logarithms that states:
log_a(x) = log_a(y) if and only if x = y.
Given the equation: log4(4+7x) = log4(5-x)
We can rewrite it as: 4+7x = 5-x
Now, solve for x:
7x + x = 5 - 48x = 1x = 1/8
Therefore, the solution to the equation log4(4+7x) = log4(5-x) is x = 1/8.
To solve this logarithmic equation, we first need to use the property of logarithms that states:
log_a(x) = log_a(y) if and only if x = y.
Given the equation: log4(4+7x) = log4(5-x)
We can rewrite it as: 4+7x = 5-x
Now, solve for x:
7x + x = 5 - 4
8x = 1
x = 1/8
Therefore, the solution to the equation log4(4+7x) = log4(5-x) is x = 1/8.