Question #03bcb

1 Answer
Harold Walden
Mar 28, 2017

#a=(2ln5+ln2)/(5ln5-2ln2)#

Explanation:

Take the natural logarithm of both sides.
#ln(5^(5a-2))=ln(2^(2a+1))#
Use the log law #log(a^b)=blog(a)# to make the index a coefficient.
#(5a-2)ln(5)=(2a+1)ln(2)#
Expand Brackets
#5aln(5)-2ln(5)=2aln(2)+ln(2)#
Combine like terms on either side of equality
#5aln(5)-2aln(2)=2ln(5)+ln(2)#
Factorise by a on the left hand side
#a[5ln(5)-2ln(2)]=2ln(5)+ln(2)#
Divide both sides by #5ln(5)-2ln(2)#
#(a[5ln(5)-2ln(2)])/(5ln(5)-2ln(2))=(2ln(5)+ln(2))/(5ln(5)-2ln(2))#
Cancelling on left hand side leaves;
#a=(2ln5+ln2)/(5ln5-2ln2)#

Hope that helps :)

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