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Hi, need help with solving this logarithm.​

Hi, need help with solving this logarithm.​-example-1

1 Answer

4 votes

Answer:


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

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^{(1)/(2)})^7


\log 8 - \log x + 7\log\sqrt x =\log 8 - \log x + \log x^(7)/(2)

Apply quotient and product rule of logarithm


\log 8 - \log x + 7\log\sqrt x =\log ((8*x^(7)/(2))/(x) )

Apply law of indices


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

Solve exponent


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


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


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

User Sgcharlie
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