Question

considere
log 2= 0,3
log 5= 0,7
log 7 =0,8

determine:
a) log{5} 28=

b) log{8} 14=

Answer 1

$\mathsf{log_5(28)= \dfrac{log(28)}{log(5)} }\\\\ \mathsf{log_5(28)= \dfrac{log(2^2\cdot7)}{log(5)} }\\\\ \mathsf{log_5(28)= \dfrac{log(2)^2+log(7)}{log(5)} }\\\\ \mathsf{log_5(28)= \dfrac{2\cdot log(2)+log(7)}{log(5)} }\\\\ \mathsf{log_5(28)= \dfrac{2\cdot0,3+0,8}{0,7} }\\\\ \mathsf{log_5(28)= \dfrac{0,6+0,8}{0,7} }\\\\ \Large\boxed{\mathsf{log_5(28)=2}}$


$\mathsf{log_8(14)= \dfrac{log(14)}{log(8)} }\\\\ \mathsf{log_8(14)= \dfrac{log(2\cdot7)}{log(2)^3} }\\\\ \mathsf{log_8(14)= \dfrac{log(2)+log(7)}{3\cdot log(2)} }\\\\ \mathsf{log_8(14)= \dfrac{0,3+0,8}{3\cdot0,3} }\\\\ \Large\boxed{\mathsf{log_8(14)\approx1,2}}$