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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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Answer:

Therefore the amount in the 4% savings account = $550

Step-by-step explanation:

i) the total amount = $1500

ii) let the amount placed in the 4% interest savings account = x

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iv) therefore fro i) we can say  x  +  y = 1500

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A rectangular paperboard measuring 29in long and 20in wide has a semicircle cut out of it, as shown below.
katen-ka-za [31]

Here, we are required to find the area of the paper board given after the semicircle is cut out of it

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Area of the paper board that remains = Area of a rectangle - Area of a semi circle

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brainly.com/question/16994941

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