How do you solve #13^v=76#?

2 Answers
Alan P.
Aug 24, 2016

#v=log_13 76 ~~1.6884#

Explanation:

You probably need to use a calculator or spreadsheet to evaluate the base 13 log.

Gió
Aug 24, 2016

I found: #v=1.68843#

Explanation:

I would try using logarithms.
Take the log in base #13# on both sides:
#log_(13)(13^v)=log_(13)(76)#
On the left we can write:
#vlog_(13)(13)=log_(13)(76)#
with: #log_(13)(13)=1#
so:
#v=log_(13)(76)#
now we seem stuck but if we have a calculator we can change base and evaluate it:
#v=(ln(76))/(ln(13))=1.68843#

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