Question

log of 24^1/8 = ?



(step by step answer please)




​

Answer 1

$log{(24)}^{ \frac{1}{8} }$

$\purple{ \sf{since : }}$

$\red{ \boxed{ log(a)^{m} = m log(a) }}$

$\implies \frac{1}{8} \times log(24)$

$\implies \frac{1}{8} \times log(8 \times 3)$

$\purple{ \sf{since : }}$

$\red{ \boxed{ log(a \times b) = log(a) + log(b) }}$

$\implies\frac{1}{8} [ log(8) + log(3) ]$

$\implies\frac{1}{8} [ log( {2)}^{3} + log(3) ]$

$\implies\frac{1}{8} [ 3log( {2)} + log(3) ]$

$\purple{ \sf{ since : }}$

$\red{ \boxed{ log(2) = 0.3010}}$

$\red{ \boxed{ log(3) = 0.4771}}$

$\implies\frac{1}{8} [ 3(0.3010) + 0.4771 ]$

$\implies\frac{1}{8} [ 0.903 + 0.4771 ]$

$\implies\frac{1}{8} [ 1.3801 ]$

$\orange{ \therefore 0.173} \: \: ( \sf{approx.)}$

HOPE IT HELPS!!