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WINSTONCH [101]
2 years ago
13

Can SOMEBODYYY please do the maths!!! PLeassssssssssssseeeeeeee

Mathematics
1 answer:
Anna11 [10]2 years ago
5 0

Answer:

<h2>see below</h2>

Step-by-step explanation:

<h3>Question-6:</h3>

we are given a equation

\sf \displaystyle \:   \log_{4}( - x)  +   \log_{4}( 6 - x)   = 2

to solve so

recall logarithm multiplication law:

\sf \displaystyle \:   \log_{4}( - x \times (6 - x))  = 2

simplify multiplication:

\sf \displaystyle \:   \log_{4}(  - 6 x +   {x}^{2} )  = 2

remember \displaystyle \log_{4}(4^2)=2

so

\sf \displaystyle \:   \log_{4}(  - 6 x +   {x}^{2} )  =     \log_{4}( {4}^{2} )

cancel out \log_4 from both sides:

\sf \displaystyle \:    - 6 x + {x}^{2}   =      {4}^{2}

simplify squares:

\sf \displaystyle \:    - 6 x + {x}^{2}   =      16

move left hand side expression to right hand side and change its sign:

since we are moving left hand side expression to right hand side there'll be only 0 left in the left hand side

\sf \displaystyle \:    - 6 x + {x}^{2}  - 16  =     0

rewrite it to standard form i.e ax²+bx+c=0

\sf \displaystyle \:      {x}^{2} - 6x  - 16  =     0

rewrite -6x as 2x-8x:

\sf \displaystyle \:      {x}^{2}   + 2x  -  8x  - 16  =     0

factor out x and 8:

\sf \displaystyle \:    x  {(x}^{}   +  2)  - 8(x   + 2) =     0

group:

\sf \displaystyle \:    (x    -  8){(x}^{}   + 2) =     0

\displaystyle \: x = 8 \\ x = - 2

\therefore \: x =  - 2

<h3>Question-7:</h3>

move left hand side log to right hand side:

\displaystyle \:   \log(x ) +  \log(x - 21)  = 2

use mutilation logarithm rule;

\displaystyle \:   \log( {x}^{2} - 21x)  = 2

\log(10^2)=2 so

\displaystyle \:   \log( {x}^{2} - 21x)  =  \log({10}^{2} )

cancel out log from both sides:

\displaystyle \:   {x}^{2} - 21x =  100

make it standard form:

\displaystyle \:   {x}^{2} - 21x  - 100=  0

factor:

\displaystyle \:   {(x} + 4)(x - 25)=  0

so

\displaystyle \:   x = 25

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