Find the value of loga81 given that loga3=1.618

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To answer this question, use the following rule of logarithms:

`log_a x^b = blog_a x`

This means that logarithm of any base of a number taken to the power b equals b multiplied by the logarithm of the same base of that number.

In this case, the number is 3, and the logarithm of the base a of 3 is given: `log_a 3 = 1.618`

The number 81 is a power of 3: ` `

`3^4 = 81`

So, the logarithm of base a of 81 can be rewritten, using the above rule, as

`log_a 81 = log_a 3^4 = 4log_a 3`

and calculated as 4(1.618) = 6.472.

Therefore, the value of

`log_a 81`

is 6.472.

Approved by eNotes Editorial Team

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