Question

Question #03bcb

Answer 1

`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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