Question

Given the exponential equation 3x = 243, what is the logarithmic form of the equation in base 10?

Answer 1

I got B as my answer

Answer 2

Am i correct

Answer 3

\(\large\color{black}{ 3^x=243}\) gives \(\large\color{black}{ \log 243=x \log }3\)

\(\large\color{black}{ \log 243=x \log }3\)
\(\large\color{black}{ \log 243 \div \log3=x }\) or
\(\large\color{black}{ \log _3243=x }\)

Answer 4

Yes you are

Answer 5

Thanks once again!

Answer 6

I would just say that 243 = 3^5 if I was to solve it. No trig solutions to algebra

Answer 7

yw

Answer 8

If we take the log (base 10) of both sides we have:
log (base 10) 3^x = log (base 10) 243
Using the law that says log a^b = b*log a we have:
x*log (base 10) 3 = log (base 10) 243
x = [log (base 10) 243]/[log (base 10) 3]
x = [log (base 10 (2.43*100)]/[log (base 10) 3]
Using the law that says log (a*b) = log a + log b:
x = [log (base 10) 2.43 + log (base 10) 100]/[log (base 10) 3]
Since the log (base 10) of 100 = 2 (remember 10^2 = 100 so the log (base 10) of 100 = 2):
x = [(log (base 10) 2.43) + 2]/[log (base 10) 3.
Look up the base 10 logs for 2.43 and 3 and finish the calculation.

Answer 9

wow... if I didn't know how to do this on my own, this would scare me so much !

Answer 10

what you mean this is wrong?