Use properties of logarithms to find the exact value of the expression.

(log3(81)^4

I think you mean

log3(81)^4

4 log3(81)

find log3(81) first
3^(log 3(81)) = 81

but 81 = 9*9 = 3^4
so log3(81) = 4

so we have
4 * 4 = 16

I meant it the way it is written. The book answer is 256. In excel, it confirms that the answer is 256.

(log3 81)^4 , ((log3 81)=4 by definition)

= (4)^4
= 256

Hi, I have the same problem, but could you show the solutions in terms of "Properties of Logarithms"

Thanks,
Chelsea

ghyguh

To find the exact value of the expression (log3(81))^4 using properties of logarithms, we can start by rewriting the expression.

First, let's simplify the logarithm. Since log3(81) means "what power of 3 gives us 81," we know that 3^4 = 81. Therefore, log3(81) = 4.

So, the expression (log3(81))^4 can be rewritten as 4^4.

Now, we simply calculate 4^4, which equals 256.

Therefore, the exact value of the expression (log3(81))^4 is 256.