Question

Log 1/15 (225 корень 3 степени из 15)

Answer 1

$=log_{15^{-1}}(15^2*15^{ \frac{1}{3} } )=-1*log_{15}(15^{2+ \frac{1}{3}} ) = \\ -1*log_{15}(15^{ \frac{7}{3}} ) = -1*\frac{7}{3}*log_ {15}(15)=-\frac{7}{3}$

Answer 2

To simplify the expression, we can convert the given expression to logarithmic form. The expression "log base b of x" can be written as "log(x) base b".

Therefore, we can rewrite the expression "log 1/15 (225√(3^15))" as:

log (225√(3^15)) base 1/15

Using the logarithmic property, we can rewrite the expression as:

log (225√(3^15)) / log (1/15)

Now, let's simplify the numerator and denominator separately.

Numerator: log (225√(3^15)) = log (225 * (3^15)^(1/2))

Using the logarithmic property log(ab) = log(a) + log(b), we can rewrite the numerator as:

log 225 + log ((3^15)^(1/2))

Simplifying further:

log 225 + (1/2) * log (3^15)

Using the property log(a^b) = b * log(a), we can simplify further:

log 225 + (1/2) * 15 * log 3

Now we have simplified the numerator. Let's move on to the denominator.

Denominator: log (1/15)

Using the property log(1/a) = -log(a), we can rewrite the denominator as:

-log 15

Now we have simplified both the numerator and denominator. Let's combine them:

(log 225 + (1/2) * 15 * log 3) / -log 15

Please note that this is the simplified form of the expression. If you need a numerical value, you can evaluate it using a calculator.