Determine whether the following statement is true or false, and explain why.

Emeli Hagan

Emeli Hagan

Answered question

2021-10-12

Determine whether the following statement is true or false, and explain why.
ln4ln8=ln4ln8

Answer & Explanation

smallq9

smallq9

Skilled2021-10-13Added 106 answers

The difference property of logarithms is lnxlny=lnxlny . This is written for natural logarithms but is true for logarithms of all bases.
An identity is true if one side of the identity can be converted to the expression on the other side. Identity can be in terms of variables or constants. For example, 2+2=4 is an identity involving constants, while (A+B)2=A2+2AB+B2 is an identity involving variables.
Step 2
Given statement is ln4ln8=ln4ln8
By difference property of logarithms this statement could have been true if it had been instead ln48=ln4ln8
So, the given statement is false. Show this by simplifying each side. First simplify the left hand side.
ln4ln8=ln22ln23
=2ln23ln2
=23
Now simplify the right hand side.
ln4ln8=ln48
=ln12
0.693147
HEnce, right hand side is a negative number while left hand side is a positive number.
Hence, given statement is false.

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