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Misha Larkins [42]
3 years ago
15

Hi, need help with solving this logarithm.​

Mathematics
1 answer:
vfiekz [6]3 years ago
8 0

Answer:

\log 8 - \log x + 7\log\sqrt x =\log (8x^{\frac{5}{2}})

Step-by-step explanation:

Given

\log 8 - \log x + 7\log\sqrt x

Required

Express as a single expression

We have:

\log 8 - \log x + 7\log\sqrt x

Write 7 as an exponent

\log 8 - \log x + 7\log\sqrt x =\log 8 - \log x + \log(\sqrt x)^7

Rewrite as:

\log 8 - \log x + 7\log\sqrt x =\log 8 - \log x + \log(x^{\frac{1}{2}})^7

\log 8 - \log x + 7\log\sqrt x =\log 8 - \log x + \log x^\frac{7}{2}

Apply quotient and product rule of logarithm

\log 8 - \log x + 7\log\sqrt x =\log (\frac{8*x^\frac{7}{2}}{x} )

Apply law of indices

\log 8 - \log x + 7\log\sqrt x =\log (8*x^{\frac{7}{2} - 1})

Solve exponent

\log 8 - \log x + 7\log\sqrt x =\log (8*x^{\frac{7-2}{2}})

\log 8 - \log x + 7\log\sqrt x =\log (8*x^{\frac{5}{2}})

\log 8 - \log x + 7\log\sqrt x =\log (8x^{\frac{5}{2}})

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Answer:

1.) slope=2

2.) slope=-3

3.) slope=\frac{1}{4}

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Step-by-step explanation:

The unit rate is also known as slope. Slope is the change in the y values over the change in the x values:

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However, with certain graphs, the slope can be found in a simpler manner.

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