Question

x= (-4ln(5)-1ln(4))/(ln(5)-2ln(4))=(4ln(5)+1ln(4))/(2ln(4)-ln(5))

Answer 1

The second expression after equals is an identity of the first so x=(4ln(5)+ln(4))/(2ln(4)-ln(5))=

ln((5^4)*4)/ln(4^2/5)=ln(625*4)/ln(16/5)=ln(2500)/ln(3.2)=6.7266 approx. The answer would be the same for log to any base. (Using base 10 logs, for example, we would be able to write 2500 as 10000/4 and log10000=4, so log2500=4-log4, or 4-2log2; log3.2=5log2-1; x=(4-2log2)/(5log2-1)=6.7266. Only one log is required in this expression.)