Question

Log2 56+4 log4 12-log2 63

Answer 1

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Answer 2

To simplify the expression, let's use the properties of logarithms. Remember the following properties:

1. log_b(x) + log_b(y) = log_b(xy) (Product Rule)
2. log_b(x) - log_b(y) = log_b(x/y) (Quotient Rule)
3. log_b(x^c) = c * log_b(x) (Power Rule)

Now, let's simplify the expression step by step:

1. log2(56) + 4 * log4(12) - log2(63)

Step 1: Simplify the logarithms with bases other than 10 or e. 2. log2(2^3 * 7) + 4 * log4(2^2 * 3) - log2(3^2 * 7)

Step 2: Apply the power rule to move the exponent as a coefficient. 3. 3 * log2(2) + 4 * 2 * log4(2) - 2 * log2(3) - log2(7)

Step 3: Simplify the logarithms with known values. 4. 3 * 1 + 8 * 1/2 - 2 * log2(3) - log2(7)

Step 4: Perform the calculations. 5. 3 + 4 - 2 * log2(3) - log2(7)

Step 5: Evaluate the logarithms. 6. 3 + 4 - 2 * log(3) - log(7) (Since log2 is the same as log base 2)

Step 6: Finally, calculate the result. 7. 7 - 2 * log(3) - log(7)

This is the simplified expression: 7 - 2 * log(3) - log(7).