Question

Solve the equation: log⁡(3k^3 )=log⁡(k)+log⁡(16)+log⁡(k)

Answer 1

Answer:

5.333....

Step-by-step explanation:

Use the product policy of logarithms,

$\tt{log\;_b(x)+log\;_b(y)=log\;_b(xy)}$

$\implies\tt{log(3k^3)=log(k)+log(16)+log(k)}\\\\\implies\tt{log(3k^3)=log(k.16.k)}$

$\implies\tt{log(3k^3)=log(16k^2)}$

For the equation to be equal, the argument of logarithms on both sides of the equation must be equal.

$\implies\tt{3k^3=16k^2}$

$\implies\tt{3k^3-16k^2=0}\\\\\implies\tt{k^2(3k-16)=0}\\\\\implies\tt{k^2=0\qquad or, \qquad 3k-16=0}\\\\\implies\tt{k=0\;or\;\dfrac{16}{3}}$

Exclude the solutions that do not make this equation true.

$\tt{\therefore k = \dfrac{16}{3}=5\dfrac{1}{3}=5.333...}$