logb x= logb(x+2)-logb8
What is the question?
logb x= logb(x+2)-logb8
logx = log [ (x+2)/8 ] , where all logs are base 8
anti-log it
x = (x+2)/8
8x = x+2
7x = 2
x = 2/7
To solve for x in the equation logb x = logb(x+2) - logb 8, we will use properties of logarithms and algebraic simplifications. Remember that logarithms represent the exponent to which the base b must be raised to obtain the value inside the logarithm.
Step 1: Apply the quotient rule of logarithms
Using the quotient rule, we can rewrite the equation as a single logarithm by subtracting the logarithm on the right side.
logb x = logb((x+2)/8)
Step 2: Remove the logarithm by setting the bases equal
Since the bases are the same, we can remove the logarithms and set the expressions inside the parentheses equal to each other.
x = (x+2)/8
Step 3: Solve for x
To solve for x, we will multiply both sides by 8 to eliminate the fraction.
8x = x + 2
Step 4: Simplify and isolate x
Combine like terms on the right side of the equation.
7x = 2
Step 5: Divide both sides by 7
Divide both sides of the equation by 7 to solve for x.
x = 2/7
Therefore, the solution to the equation logb x = logb(x+2) - logb 8 is x = 2/7.