This Problem is extremley confusing could someone help? Thank you so much for your time!
Write each log as a common log:
log2(x) = log(x) / log(2)
log3(x) = log(x) / log(3)
log4(x) = log(x) / log(4)
log5(x) = log(x) / log(5)
On the left-hand side, we will end with: [ log(x) ]4 / [ log(2) · log(3) · log(4) · log(5) ]
On the right-hand side, we will need to multiply each term by an appropriate term to get the common denominator
of [ log(2) · log(3) · log(4) · log(5) ].
Multiply the first term by log(5) / log(5)
the second term by log(4) / log(4)
the third term by log(3) / log(3)
the fourth term by log(2) / log(2)
Adding those terms together, you will end with the numerator of [ log(x) ]3 · [ log(2) + log(3) + log(4) + log(5) ]
Setting the two numerators together: [ log(x) ]4 = [ log(x) ]3 · [ log(2) + log(3) + log(4) + log(5) ]
Dividing out [ log(x) ]3 , we get log(x) = log(2) + log(3) + log(4) + log(5)
log(x) = log(120)
x = 120