Question

An electronic engineering technician has been asked to determine the signal-to-noise

ratio value of a signal generator.
Four signal generators have been tested, and the results of the tests can be represented by
2log3 + log4 = logA + 4log2
4 Solve the equation to find the value of A.
Show evidence of the use of the laws of logarithms in your answer.

Answer 1

Using the properties of logarithms to simplify the given equation. We find that A = 2.25

Step-by-step explanation:

To solve the equation 2log3 + log4 = logA + 4log2 for the value of A, we can use the properties of logarithms to simplify the equation.

Using the property log(a) + log(b) = log(a * b), we can rewrite the equation as :

log(32) + log(4) = log(A) + log(24)

Further simplifying, we get log(9) + log(4) = log(A) + log(16)

Using the property log(a) + log(b) = log(a * b), we can combine the logs on the left-hand side to get:

log(9 * 4) = log(A * 16)

Simplifying further, we have log(36) = log(16A)

Since the bases are the same, the equation is true if the arguments are equal, so 36 = 16A

Dividing both sides by 16, we find that A = 2.25