What is the inverse of f(x)=3+2lnx in radical form

1 answer:

8 0

$f(x)=3+2\ln x,\ x > 0\\\\y=3+2\ln x\\\\\text{replace x with y and y with x}\\\\3+2\ln y=x\ \ \ \ |-3\\\\2\ln y=x-3\ \ \ \ |:2\\\\\ln y=\dfrac{y-3}{2}\to e^{\ln y}=e^{\frac{y-3}{2}}\\\\y=e^{\frac{y-3}{2}}\\\\Answer:\ f^{-1}(x)=e^{\frac{y-3}{2}}$

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postnew [5]

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$\\ \sf\longmapsto \dfrac{(0.15)^{2\times \dfrac{-3}{2}}\times (0.1)^{4\times \dfrac{3}{4}}}{(0.5)^{3\times \dfrac{1}{3}}}$

$\\ \sf\longmapsto \dfrac{(0.15)^{-3}(0.1)^3}{(0.5)^1}$

$\\ \sf\longmapsto \dfrac{\dfrac{1}{(0.15)^3}\times 0.001}{0.5}$

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$\\ \sf\longmapsto\dfrac{ \dfrac{1000000}{3375}\times \dfrac{1}{1000}}{0.5}$

$\\ \sf\longmapsto \dfrac{\dfrac{1000}{3375}}{0.5}$

$\\ \sf\longmapsto \dfrac{1000}{3375}\times \dfrac{10}{5}$

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4 0

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An electron has an atomic mass of 5.4 x 10-4. If a carbon atom has 6 electrons, what is the combined atomic mass of the electron

Gwar [14]

<span>6*5.4*10^(-4)
=32.4*10^(-4)
move the decimal point, in scientific notation you only have a single digit with comma
=3.2*10^(-3)

so option A

to know if you have to increase or decrease the exponent you can write the intermediary steps out:</span>
32.4*10^(-4)=32.4/10^4=<span>(3.24*10)/(10*10^3)
reduce the fraction and you have the above solution
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