How do you solve #3^x=729#?

2 Answers
Jan 17, 2017

Multiply each side by #log_10# . Eventually, x = 6

Explanation:

Usually, just log means #log_10#, so we can multiply both sides by log.
#log3^x = log 729#
Then, with the log law, we can move the exponent x to the left of log3.
#xlog3 = log729#
Since the x is attached by multiplication, we can divide both sides by log 3.
#x = log(729)/log(3)#
Plug into your calculator and voila!
#x = 6#

I used log since this question was posted in log, but you could also solve by making 729 base 3, then set the exponents equal to each other.
#3^x = 3^6#
#x = 6#
You could also say #x = log_3 (729)# (by using the log function) and plug that into your calculator as well.

Aug 5, 2018

#x=6#

Explanation:

We can rewrite #729# as #3^6#. With this in mind, we now have

#3^x=3^6#

Since the bases are the same, we can equate the exponents. We get

#x=6#

Hope this helps!