Question

If $(6{)}^{15}\times (10{)}^5\times (15{)}^6=2^x\times 3^y\times 5^z$ then find the value of x + y + z.

• A. $26$
• B. $52$
• C. $42$
• D. $48$

Answer 1

Answer: (B)

$52$

$(6{)}^{1}5\times (10{)}^5\times (15{)}^6=2^x\times 3^y\times 5^z$
$\Rightarrow$ $(2\times 3{)}^{15}\times (2\times 5{)}^5\times (3\times 5{)}^6=2^x\times 3^y\times 5^z$
$\Rightarrow 2^{(15+5)}{3}^{(15+6)}{5}^{(5+6)}=2^x\times 3^y\times 5^z$
$\Rightarrow 2^{20}{3}^{21}{5}^{11}=2^x\times 3^y\times 5^z$
By comparing, $x=20.y=21andz=11$
x + y + z = $20+21+11=52$