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Home Q & A Board Science-Related Homework Help Mathematics
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irina irina
wrote...
Posts: 919
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12 years ago
What is the solution (x) in this equation, correct to three decimal places:

3^x = 7

I know what the answer is, but only because it was a multiple choice question. If you could explain how you work it out, that'd be great.
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wrote...
#1
12 years ago
only because it was a multiple choice question: what are the choices my friend I need to know
3^x = 7
lg3^x = lg7 //lg both sides
xlg3 = lg7 //power law bring down x
x = lg7/lg3 = 1.7712 = 1.77 (to 3s.f.)
wrote...
#2
12 years ago
I would take the log of both sides.

3^x = 7
log(3^x) = log7

Bring the x outside, as the exponent is allowed to be brought out.

xlog3 = log7

Solve for x by isolating it; divide by log3 on both sides.

x = (log7)/(log3)

x = 1.771

Teo's is right as well, but he/she used significant figures instead of decimal places. =)
wrote...
#3
12 years ago
x log 3 = log 7
x = log 7 / log 3
x = 1.77
wrote...
#4
12 years ago
Take the natural log of both sides.

ln(3^x) = ln(7)

Due to the properties of logarithms, we can pull the x outside of the natural log.

x * ln(3) = ln(7)
x = ln(7)/ln(3) = 1.771
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