SOLUTION: Write as a single logarithm 2+(1/2)log5(x-1)-3log5(2z)+(2/3)log5(y)-log5(a)

Algebra.Com
Question 1192142: Write as a single logarithm
2+(1/2)log5(x-1)-3log5(2z)+(2/3)log5(y)-log5(a)

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!


The first term " 2 " must be written as a logarithm with base 5.  
Here is how to do that:

Let N be such that log5(N) = 2

Then by the definition of lagarithm, 52 = N,

so we write 2 as log5(52) 

Now we have:

 

We move all coefficients of logs as exponents of whatever the log is
being taken of:


 

Write all the terms that have " + " before them together and those
that have " - " before them together:

  

Group the terms with + and group those with - preceded by a minus sign:



Inside both parentheses, use the rule of logs that says
"the sum of logs is the log of the product"



Finally, use the rule of logs that says
"the difference of two logs is the log of the quotient (division)



You can finish by :

1. writing 25 as 25.
2. writing (2z)3 as 23z3 and again as 8z3



Edwin

RELATED QUESTIONS

log5^3-log5^2-log5(1/4) as a single log attempt:... (answered by MathLover1,josmiceli)
write the expression as a single logarithm. 3log5(2)+log5(7) please show steps too (answered by jim_thompson5910)
write 1 - 3 log5 x as a single... (answered by nerdybill)
Write the expression, log5(x^2-4) - log5(x+2), as a single... (answered by stanbon)
write the following expression as a single logarithm: 3log5(5 is the base)2+log5(5 is the (answered by LinnW)
Write the expression as a single logarithm log5 (x)-3 (answered by robertb)
Write as a single log:... (answered by stanbon)
Write as a single log: 1/2logx^2 - 2log(x+1) +... (answered by Fombitz)
Condense the expression. 1/3 log5 8-1/2 log5 x = 4 log5... (answered by Alan3354)