Question #03bcb

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Question #03bcb

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Answer 1 · 2017-03-28T02:46:56

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

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;
$a=(2ln5+ln2)/(5ln5-2ln2)$

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Question #03bcb

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