Question

Pregunta urgente por favor ​

Answer 1

log7(1440)=

=log7(144×10)

=log7(12^2×10)

=log7(12^2)+log7(10)

=2log7(12)+log7(2×5)

=2log7(2^2×3)+log7(2)+log7(5)

=2log7(2^2)+2log7(3)+log7(2)+log7(5)

=4log7(2)+2log7(3)+log7(2)+log7(5)

=5log7(2)+2log7(3)+log7(5)

cambiando de base a logaritmos decimales:

log7(2)=[log(2)/log(7)]

log7(3)=[log(3)/log(7)]

log7(5)=[log(5)/log(7)]

reemplazando:

=5[log(2)/log(7)]+2[log(3)/log(7)]+[log(5)/log(7)]

=[5log(2)+2log(3)+log(5)]/log7

log(2)=0,301029996

log(3)=0,477121255

log(5)=0,698970004

log(7)=0,84509804

reemplazando:

=[5(0,3010)+2(0,4771)+(9,6989)]/(0,8451)

log7(1440)=3,7373