This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
thanks for sending clearer images! I can now make out two questions. Here's how to solve the equation 3^x = 81: Step 1: Express both sides of the equation with the same base. We need to express 81 as a power of 3. 81 = 3 × 3 × 3 × 3 = 3^4 So the equation becomes: 3^x = 3^4 Step 2: Equate the exponents. If the bases are the same, then the exponents must be equal. x = 4 The solution is x = 4. --- Now, for the cone question: The height of the cone is given as h = 8 cm. From the diagram, the radius of the cone is r = 6 cm. The question likely asks for the slant height, labeled as s. Step 1: Identify the relationship between height, radius, and slant height. In a right circular cone, the height, radius, and slant height form a right-angled triangle, with the slant height being the hypotenuse. We can use the Pythagorean theorem. s^2 = h^2 + r^2 Step 2: Substitute the given values into the formula. s^2 = (8 cm)^2 + (6 cm)^2 s^2 = 64 cm^2 + 36 cm^2 s^2 = 100 cm^2 Step 3: Solve for the slant height s. Take the square root of both sides: s = sqrt(100 cm)^2 s = 10 cm The slant height of the cone is 10 cm. --- I'm still unable to fully read the logarithm question due to the blurriness of the denominator. If you can type it out, I'd be happy to help! What's next? Send 'em.