The volume of two similar solid' spheres are 4752 cm³ and 1408 cm³. If the surface area of the smaller sphere is 352 cm², find the surface area of the larger sphere.

Huu hapa ni utatuzi wa swali lako:

2. Eleza $\frac{\log_{10} 63}{\log_{10} 147}$ kwa kutumia $x$ na $y$.

• Step 1: Andika nambari 63 na 147 kama bidhaa za vigawo vikuu. $63 = 9 \times 7 = 3^2 \times 7$ $147 = 3 \times 49 = 3 \times 7^2$

• Step 2: Rahisisha $\log_{10} 63$ kwa kutumia sheria za logariti. Tunajua $\log_{10} 3 = x$ na $\log_{10} 7 = y$.

  $$\log_{10} 63 = \log_{10} (3^2 \times 7)$$

  Tumia sheria ya kuzidisha ya logariti ($\log_b (MN) = \log_b M + \log_b N$):

  $$\log_{10} (3^2 \times 7) = \log_{10} (3^2) + \log_{10} 7$$

  Tumia sheria ya nguvu ya logariti ($\log_b (M^p) = p \log_b M$):

  $$\log_{10} (3^2) + \log_{10} 7 = 2 \log_{10} 3 + \log_{10} 7$$

  Badilisha $x$ na $y$:

  $$2x + y$$

• Step 3: Rahisisha $\log_{10} 147$ kwa kutumia sheria za logariti.

  $$\log_{10} 147 = \log_{10} (3 \times 7^2)$$

  Tumia sheria ya kuzidisha ya logariti:

  $$\log_{10} (3 \times 7^2) = \log_{10} 3 + \log_{10} (7^2)$$

  Tumia sheria ya nguvu ya logariti:

  $$\log_{10} 3 + \log_{10} (7^2) = \log_{10} 3 + 2 \log_{10} 7$$

  Badilisha $x$ na $y$:

  $$x + 2y$$

• Step 4: Andika usemi wa mwisho. Sasa tunaweza kuandika usemi wa asili kwa kutumia $x$ na $y$:

  $$\frac{\log_{10} 63}{\log_{10} 147} = \frac{2x + y}{x + 2y}$$

  Usemi katika $x$ na $y$ ni $\boxed{\frac{2x + y}{x + 2y}}$.