Question

determine b if log b to the base√8=10/3​

Answer 1

Answer:

32

Step-by-step :

Log b to base √8=10/3

Log b to base 8^1/2 = 10/3

We can write this as log b = 8^1/2×10/3

b = 8^5/3

b = 32

Answer 2

$\bold{ log_{ \sqrt{8} }(b ) = \frac{10}{3} }$

$\implies \: { \sqrt{8} }^{ \frac{10}{3} } = b$

$\implies \: { {8} }^{ \frac{10}{3}×\frac{1}{2} } = b$

$\implies \: { {2³} }^{ × \frac{10}{3}×\frac{1}{2} } = b$

$\implies \: { {2⁵} } = b$

$\implies \: \boxed{\bold { b = {32} }}$