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ScanSolve AI Answer
Here's the continuation of the previous answer: FURTHER LOGARITHMS 3. Find the value of x given that (15 - 5x) - 1 = (3x - 4). (Assuming base 10 for ) Step 1: Express 1 as a logarithm with base 10. 1 = _10 10 Step 2: Rewrite the equation. (15 - 5x) - 10 = (3x - 4) Step 3: Apply the logarithm property a - b = ((a)/(b)) on the left side. ((15 - 5x)/(10)) = (3x - 4) Step 4: Equate the arguments of the logarithms. (15 - 5x)/(10) = 3x - 4 Step 5: Solve the resulting algebraic equation. 15 - 5x = 10(3x - 4) 15 - 5x = 30x - 40 15 + 40 = 30x + 5x 55 = 35x x = (55)/(35) x = (11)/(7) Step 6: Check for valid solutions. The arguments of logarithms must be positive. For (15 - 5x): 15 - 5x > 0 15 > 5x x < 3. For (3x - 4): 3x - 4 > 0 3x > 4 x > (4)/(3). Our solution x = (11)/(7) ≈ 1.57. This value satisfies both x < 3 and x > (4)/(3). x = (11)/(7) Last free one today — make it count tomorrow, or type /upgrade for unlimited.