Question

Log6 (x+8)-log63-log67

Answer 1

To solve the expression log6(x+8) - log63 - log67, we can use logarithmic properties to simplify the expression.

Step 1: Apply the quotient rule

The quotient rule states that log(a) - log(b) = log(a/b). Using this rule, we can rewrite the expression as:

log6(x+8) - log63 - log67 = log6((x+8)/(3*7))

Step 2: Simplify the expression

To simplify further, we can simplify the numerator and denominator separately:

Numerator: (x+8) Denominator: 3 * 7 = 21

So the simplified expression becomes:

log6((x+8)/(3*7)) = log6((x+8)/21)

This is the simplified form of the given expression.

Please note that without a specific value for x, we cannot further evaluate the expression numerically. However, by simplifying the expression, we have transformed it into a more manageable form.