How do you solve log107=log10xlog102?

1 Answer
Oct 10, 2015

x=14

Explanation:

For two logarithms of the same base, logaM=logaNM=N

Using the Quotient Law, logaxlogay=loga(xy)

So,

log107=log10(x2)
7=x2
x=72
x=14

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ABR May I suggest another approach:

Logs are indices in another form as such adding indices is another representation of multiplication. Like wise, subtraction is another representation of division. Consequently:

It is given that log7=logxlog2

( it does not matter a bout what the base is in this context)

Antilog(log7)=7,Antilog(logx)=x,Antilog(log2)=2

Thus log7=logxlog2 is equivalent to 7=x2

From this it is a simple matter of manipulation to find x