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6. Estimate the Value to Three Decimal Places. A) Log_(3)53 C) Log_(6)159 B) Log_(4)(1)/(10) D) Log_(15)1456

Question

6. Estimate the value to three decimal places. a) log_(3)53 c) log_(6)159 b) log_(4)(1)/(10) d) log_(15)1456

Solution

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Answer

### a) 3.613### b) -1.661### c) 2.829### d) 2.689

Explanation

## Step 1: Change of Base Formula### We will use the change of base formula, which states , where can be any base. We will use base 10 (common logarithm) for our calculations.## Step 2: Calculate ### Using the change of base formula: ## Step 3: Calculate ### Using the change of base formula: ## Step 4: Calculate ### Using the change of base formula: ## Step 5: Calculate ### Using the change of base formula: