Question

5^w × 7^x × 2^y × 3^z = 36^3 × 35^2 × 30^2 × 21 is , what is the value of y​

Answer 1

Answer:

$5^w × 7^x × 2^y × 3^z = 36^3 × 35^2 × 30^2 × 21$

Solving RHS

$= 36^3 × 35^2 × 30^2 × 21 \\ \\ \\ = (6 \times 6) {}^{3} \times (7 \times 5) {}^{2} \times (6 \times 5) {}^{2} \times (7 \times 3) \\ \\ \\ = 6 {}^{3} \times 6{}^{3} \times 7 {}^{2} \times {5}^{2} \times 6 {}^{2} \times {5}^{2} \times 7 \times 3 \\ \\ \\ = 6 {}^{3} \times {6}^{3} \times {6}^{2} \times {5}^{2} \times {5}^{2} \times {7}^{2} \times 7 \times 3 \\ \\ = 6 {}^{8} \times {5}^{4 } \times {7}^{3} \times 3 \\ \\ = (2 \times 3) {}^{8} \times {5}^{4 } \times {7}^{3} \times 3 \\ \\ = {2}^{8} \times {3}^{8} \times {5}^{4} \times {7}^{3} \times 3 \\ \\ = {2}^{8} \times {3}^{8} \times 3 \times 5 {}^{4} \times {7}^{3} \\ \\ = {2}^{8} \times {3}^{9} \times 5 {}^{4} \times {7}^{3}$

On compairing RHS with LHS

$5^w × 7^x × 2^y × 3^z= {2}^{8} \times {3}^{9} \times 5 {}^{4} \times {7}^{3} \\ \\ we \: get \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ 5 {}^{w} = {5}^{4} \: so \: \: \: \: \: w \: = 4 \\ \\ 7 {}^{x} = {7}^{3} \: \: so \: \: \: x = 3 \\ \\ \\ 2 {}^{y} = {2}^{8} \: \: so \: \: \: y = 8 \\ \\ {3}^{z} = {3}^{9} \: \: so \: \: \: z = 9$