Solve for x

Question

the question contains logarithms and I don't know how to solve them. Can you please help explain this? 

Answer 1

Apply these properties to logarithms.  This will help simplify the equations.

 

For logs and ln:

 

log(x) = y      --->   10^y = x

 

log_a(x) = y     ---->   a^y = x

 

ln(x) = y       ----->  e^y = x

 

In summary, the solution to a logarithm is the exponent of the log's base number.  Notice that the log has the base number 10 (unless the base is specified), and the ln ALWAYS has the base number e.

 

 

Properties of addition and subtraction.  The product of the log's argument is the sum of the logs.  The quotient of the log's argument is the difference between the logs.

 

log(xy) = log(x) + log(y)

 

ln(xy) = ln(x) + ln(y)

 

log(x / y) = log(x) - log(y)

 

ln(x / y) = ln(x) - ln(y)

 

 

For exponents.  The exponent of the logs argument is the coefficient of the log.

 

log(x^a) = alog(x)

 

ln(x^a) = aln(x)

 

 

 

If you have an equation such that

 

log(a) = log(b) , then

 

a = b

 

 

This also applies to ln.