precal
posted by melek .
Find the solution of the exponential equation, correct to four decimal places.
4^(2x − 1) = 6

log ( a ^ n ) = n * log ( a )
( 2 x  1 ) * log ( 4 ) = log ( 6 ) Divide both sides by log ( 4 )
2 x  1 = log ( 6 ) / log ( 4 )
2 x = log ( 6 ) / log ( 4 ) + 1
2 x = log ( 6 ) / log ( 4 ) + log ( 4 ) / log ( 4 )
2 x = [ log ( 6 ) + log ( 4 ) ] / log 4
2 x = log ( 24 ) / log ( 4 ) Divide both sides by 2
x = [ log ( 24 ) / log ( 4 ) ] / 2
x = log ( 24 ) / 2 log ( 4 )
Remark:
log ( a ) + log ( b ) = log ( a * b )
log ( 4 ) + log ( 6 ) = log ( 6 * 4 ) = log ( 24 )