How do you solve $6 {log}_{3} (0.5 x) = 11$ $6log_3(0.5x)=11$ ?

Question

4610 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-04T05:57:48

$x = 2 \times 3^{\frac{11}{6}} ≅ 2 \times 7.5 ≅ 15$ $x=2xx3^(11/6)~=2xx7.5~=15$

Let's approach it by first dividing through by 6:

$6 {log}_{3} (0.5 x) = 11$ $6log_3(0.5x)=11$

${log}_{3} (0.5 x) = \frac{11}{6}$ $log_3(0.5x)=11/6$

We can now make both sides the exponent of a base 3 (which will be the inverse function for the left hand side and cancel out the log):

$3^{{log}_{3} (0.5 x)} = 3^{\frac{11}{6}}$ $3^(log_3(0.5x))=3^(11/6)$

$0.5 x = 3^{\frac{11}{6}}$ $0.5x=3^(11/6)$

$x = 2 \times 3^{\frac{11}{6}} ≅ 2 \times 7.5 ≅ 15$ $x=2xx3^(11/6)~=2xx7.5~=15$

How do you solve 6log_3(0.5x)=116log3(0.5x)=116log_3(0.5x)=11?