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DedPeter [7]
3 years ago
10

Step by step workout of ; log x^3+log 5x=5 log 2-log 2/5

Mathematics
1 answer:
Charra [1.4K]3 years ago
4 0

Answer:

x = 2

Step-by-step explanation:

log  \: {x}^{3}  + log \: 5x = 5log \: 2 - log \:  \frac{2}{5}  \\  \\  \therefore \: log( {x}^{3}  \times 5x) = log  {2}^{5} - log \:  \frac{2}{5}  \\  \\ \therefore \: log( 5{x}^{4}) = log 32 - log \:  \frac{2}{5} \\  \\ \therefore \: log( 5{x}^{4}) = log  \bigg(32  \times  \frac{5}{2}  \bigg) \\  \\ \therefore \: log( 5{x}^{4}) = log  \bigg(16  \times  5) \\  \\ \therefore \: 5{x}^{4}=  16  \times  5 \\  \\ \therefore \: {x}^{4}=   {2}^{4}   \\  \\  \huge \purple{ \boxed{\therefore \: {x} = 2}}

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