若a,b,c為正實數且log5a=11,log25b=6,log1/5c=-13則log5(103a-b+c)最接近的整數值為?

若a，b，c為正實數且log5_a=11，log25_b=6，log(1/5)_c=－13則log5_(103a－b+c)最接近的整數值為?
Sol
log5_a=11
loga/log5=11
loga=11log5
a=5^11
log25_b=6
logb/log25=6
logb=12log5
b=5^12
log(1/5)_c=-13
logc/log5=13
logc=12log5
c=5*13
103a－b+c
=103*5^11－5^12+5^13
=5^11*(103－5+25)
=5^11*123
log5_(103a－b+c)
=log(5^11*123)/log5
=(11log5+log123)/log5
5^3=125
最接近的整數=11+3=14

(log a)/(log 5)=11
a=48828125
(log b)/(log 25)=6
b=244140625
(log c)/(log 1/5)=-13
c=1220703125
[log(103a-b+c)]/log 5
=[log(103*48828125-244140625+1220703125)]/(log 5)
=13.98997825
最接近的整數值為14