Find the base of x 73 (with base 8) = 214 (with base x)

Kenya Leonard 2022-08-01 Answered
Find the base of x
73 (with base 8) = 214 (with base x)
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Answers (1)

uavklarajo
Answered 2022-08-02 Author has 17 answers
Given what you mean is this:
log 8 73 = log x 214
Then:(use change of base formula: log a x = ln ( x ) ln ( a ) )
ln ( 73 ) ln ( 8 ) = ln ( 214 ) ln ( x )
Isolate x to one side:
ln ( 8 ) ln ( 73 ) = ln ( x ) ln ( 214 ) ln ( x ) = ln ( 8 ) ln ( 214 ) ln ( 73 )
Eliminate the logariths by rasing both sides to e:
e ln ( x ) = e ln ( ln ( 8 ) ln ( 214 ) ln ( 73 ) )
Solve:
x = ln ( 8 ) ln ( 214 ) ln ( 73 ) x = 2.60070829
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