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kakasveta [241]
3 years ago
5

Condense the following logs into a single log:

Mathematics
1 answer:
mamaluj [8]3 years ago
7 0

QUESTION 1

The given logarithm is

8\log_g(x)+5\log_g(y)

We apply the power rule of logarithms; n\log_a(m)=\log_(m^n)

=\log_g(x^8)+\log_g(y^5)

We now apply the product rule of logarithm;

\log_a(m)+\log_a(n)=\log_a(mn)

=\log_g(x^8y^5)

QUESTION 2

The given logarithm is

8\log_5(x)+\frac{3}{4}\log_5(y)-5\log_5(z)

We apply the power rule of logarithm to get;

=\log_5(x^8)+\log_5(y^{\frac{3}{4}})-\log_5(z^5)

We apply the product to obtain;

=\log_5(x^8\times y^{\frac{3}{4}})-\log_5(z^5)

We apply the quotient rule; \log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )

=\log_5(\frac{x^8\times y^{\frac{3}{4}}}{z^5})

=\log_5(\frac{x^8 \sqrt[4]{y^3} }{z^5})

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