Answer:
x = 32/5
Step-by-step explanation:
Given the logarithmic equation,
log2x + log2(x – 6) = 4, to get the equation that can solve the potential solutions to the equation we need to solve the equation by removing all traces of log as shown;
According to the law of logarithm, log a + log b = log(a/b). Applying this to the equation given
log2x + log2(x – 6) = 4,
log2(x/x-6) = 4
Also If log_a b = c, then a^c = b
x/x-6 = 2⁴
x/x-6 = 16
Cross multiplying
x = 16(x-6)
x = 16x-96
x-16x = -96
-15x = -96
x = 96/15
x = 32/5
The solution to the equation is x = 32/5
