7. Express as a single logarithm. a) log5+log11 b) log20-log4 log_(5)6+log_(5)8-log_(5)12 d) 2log3+4log2

Question

7. Express as a single logarithm. a) log5+log11 b) log20-log4 log_(5)6+log_(5)8-log_(5)12 d) 2log3+4log2

Answer 1

### a)

### b)

### c)

### d)

Answer 2

## Step 1: Applying the Product Property of Logarithms### The product property of logarithms states that

. We can apply this property to combine the sum of logarithms into a single logarithm.## Step 2: Applying the Quotient Property of Logarithms### The quotient property of logarithms states that

. We can apply this property to combine the difference of logarithms into a single logarithm.## Step 3: Applying the Power Property of Logarithms### The power property of logarithms states that

. We can apply this property to simplify logarithms with coefficients.## Step 4: Combining the Properties### We can combine the product, quotient, and power properties to simplify more complex logarithmic expressions.

Question

7. Express as a single logarithm. a) log5+log11 b) log20-log4 log_(5)6+log_(5)8-log_(5)12 d) 2log3+4log2

Solution

Answer

Explanation