Exponent problem

Algebra Level 2

$(5 \times 2) ^ { 5 \times y } = 2^y \times k ^ y$

Find the value of $\log_{10} k$ .

Note : $y\neq 0$

Use $\log _{ 10 }{ 2 } \approx0.30$ and $\log _{ 10 }{ 5 } \approx0.70$

1 solution

Eduardo Neo
Dec 23, 2016

By substitutuing $N$ in the first equation of the problem, we get :

$N={ (2 }^{ y }\ast { k }^{ y }) = { (5\ast 2) }^{ 5\ast y }$

By applying the $\log$ operator on both sides, we get :

$y*\log { 2 }+y*\log { k } =5y*\log { 10 }$ by using the symplifications the problem gives us, we get the final solution :

$\log { k } = 4.7$