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AlekseyPX
3 years ago
8

Express log0.5 in terms of a and b if a=log2 and b=log3. Thank you and please explain! :D

Mathematics
2 answers:
sweet-ann [11.9K]3 years ago
7 0

\bf \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}

\bf \log(0.5)\implies \log\left( \cfrac{1}{2} \right)\implies \log(1)-\log(2)\implies 0-a\implies -a \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log(0.5)\implies \log\left( \cfrac{1}{2} \right)\implies \begin{array}{llll} \log(1)&-&\log(2)\\\\ \log\left( 3\cdot \frac{1}{3} \right)&-&a\\\\ \log(3)+\log\left( \frac{1}{3} \right)\\\\ b+\log(3^{-1})\\\\ b+[-1\log(3)]\\\\ b+(-1b)\\\\ b-b\\ 0&-&a \end{array}


so, we can use those two methods, and we'd end up with -a anyway.

Sveta_85 [38]3 years ago
6 0

Answer:

-a

Step-by-step explanation:

\log(0.5)=\log(\frac{1}{2})=\log(1)-\log(2) By quotient rule.

\log(0.5)=\log(\frac{1}{2})=0-\log(2) Since 10^0=1.

\log(0.5)=\log(\frac{1}{2})=-\log(2)

\log(0.5)=\log(\frac{1}{2})=-a By substitution.

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Step-by-step explanation:

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Ivanshal [37]

Answer:

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Step-by-step explanation:

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What is the result of a dilation of scale factor 3 centered at the origin of the line 2y + 3x=10?? PLEASE HELP PLEASEEEEEEEEE
maks197457 [2]

Given:

The equation of a line is:

2y+3x=10

The line is dilated by factor 3.

To find:

The result of dilation.

Solution:

The equation of a line is:

2y+3x=10

For x=0,

2y+3(0)=10

2y+0=10

y=\dfrac{10}{2}

y=5

For x=2,

2y+3(2)=10

2y+6=10

2y=10-6

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Divide both sides by 2.

y=\dfrac{4}{2}

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The given line passes through the two points A(0,5) and B(2,2).

If the line dilated by factor 3 with origin as center of dilation, then

(x,y)\to (3x,3y)

Using this rule, we get

A(0,5)\to A'(3(0),3(5))

A(0,5)\to A'(0,15)

Similarly,

B(2,2)\to B'(3(2),3(2))

B(2,2)\to B'(6,6)

The dilated line passes through the points A'(0,15) and B'(6,6). So, the equation of dilated line is:

y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)

y-15=\dfrac{6-15}{6-0}(x-0)

y-15=\dfrac{-9}{6}(x)

y-15=\dfrac{-3}{2}x

Multiply both sides by 2.

2(y-15)=-3x

2y-30=-3x

2y+3x=30

Therefore, the equation of the line after the dilation is 2y+3x=30.

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3 years ago
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DanielleElmas [232]

Answer:

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Step-by-step explanation:

4/5 times 9/1 is equal to 36/5

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