How do you solve 10= 2e^ { 5x }?

2 Answers
Jim G.
Feb 5, 2018

x~~0.322" to 3 dec. places"

Explanation:

"using the "color(blue)"law of logarithms"

•color(white)(x)logx^nhArrnlogx

"divide both sides by 2"

rArre^(5x)=10/2=5

"take the ln (natural log) of both sides"

rArrlne^(5x)=ln5

rArr5xcancel(lne)^1=ln5

rArrx=ln5/5~~0.322" to 3 dec. places"

Vansh T.
Feb 5, 2018

x=ln(5)/5

Explanation:

10=2e^(5x)
or 5=e^(5x)
Take natural log on both sides
ln(5)=ln(e^(5x))

Using propertyenter image source here

ln(5)=5x*ln(e)
0r
ln(5)=5x [since ln(e)=1 ]

x=ln(5)/5

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