Solve log5(x 8) − log5(x − 8) = 2

Question

Solve the equation

x = \frac{2 lo g _{5} ( 2 ) - 6}{7}

Alternative Form

x \approx - 0.734092

Evaluate

lo g_{10} (5) \times (x \times 8) - lo g_{10} (5) \times (x - 8) = 2

Remove the parentheses

lo g_{10} (5) \times x \times 8 - lo g_{10} (5) \times (x - 8) = 2

Use the commutative property to reorder the terms

8 lo g_{10} (5) \times x - lo g_{10} (5) \times (x - 8) = 2

Move the expression to the left side

8 lo g_{10} (5) \times x - lo g_{10} (5) \times (x - 8) - 2 = 0

Calculate

More Steps

7 lo g_{10} (5) \times x + 8 lo g_{10} (5) - 2 = 0

Move the constant to the right-hand side and change its sign

7 lo g_{10} (5) \times x = 0 - (8 lo g_{10} (5) - 2)

Subtract the terms

More Steps

7 lo g_{10} (5) \times x = - 8 lo g_{10} (5) + 2

Divide both sides

\frac{7 lo g _{10} ( 5 ) \times x}{7 lo g _{10} ( 5 )} = \frac{- 8 lo g _{10} ( 5 ) + 2}{7 lo g _{10} ( 5 )}

Divide the numbers

x = \frac{- 8 lo g _{10} ( 5 ) + 2}{7 lo g _{10} ( 5 )}

Divide the numbers

More Steps

x = lo g_{5^{7}} (100 \times 5^{- 8})

Solution

More Steps

x = \frac{2 lo g _{5} ( 2 ) - 6}{7}

Alternative Form

x \approx - 0.734092

Show Solution