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andreyandreev [35.5K]

3 years ago

11

I. Describing a Translation

2 answers:

Bogdan [553]3 years ago

6 0

To find the translation you need to count how far each point is moving. It goes downwards three times while moving left 5 times, this means that the rise is negative 3 and the run is -5. (-3/-5)
I dont remember much of this but if I'm correct the formula for this coordinate notation is (x, y) -> (x - 5, y - 3) Please check this

Elza [17]3 years ago

3 0

Translation
If it’s blue to green it’s (-5,-3)

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Hello, help me please)

AlladinOne [14]

Answer:

Given equation:

$10^{5x-2}=2^{8x-3}$

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$\implies \ln 10^{5x-2}= \ln 2^{8x-3}$

$\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax$

$\implies (5x-2)\ln 10=(8x-3) \ln 2$

Expand brackets:

$\implies 5x\ln 10 - 2\ln 10=8x \ln 2 -3 \ln 2$

Collect like terms:

$\implies 5x\ln 10 - 8x \ln 2 =2\ln 10-3 \ln 2$

Factor left sides:

$\implies x(5\ln 10 - 8 \ln 2) =2\ln 10-3 \ln 2$

$\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax$

$\implies x(\ln 10^5 - \ln 2^8) =\ln 10^2- \ln 2^3$

$\textsf{Apply log Quotient law}: \quad \ln_a\frac{x}{y}=\ln_ax - \ln_ay$

$\implies x\left(\ln\left(\dfrac{10^5}{2^8}\right)\right) =\ln\left(\dfrac{10^2}{2^3}\right)$

Simplify:

$\implies x\left(\ln\left(\dfrac{3125}{8}\right)\right) =\ln\left(\dfrac{25}{2}\right)$

$\implies x=\dfrac{\ln\left(\dfrac{25}{2}\right)}{\ln\left(\dfrac{3125}{8}\right)}$

$\implies x=0.4232297737...$

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Step-by-step explanation:

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