Question 863304
write two logarithms as sums and/or differences of logarithms and simplify.
 The 2 problems i am given are a) log base 3 then in parentheses (x+3/y) all raised to the 6th power.
Assume the expression is :
{{{log(3,(((x+3)/y)^6))}}}
The log equiv of exponents, both numerator and denominator to the 6th power
{{{6log(3,((x+3)/y))}}} = {{{6log(3,(x+3))}}} - {{{6log(3,(y))}}}
:
b) is ln(e^3 times x^5/y^7 times square root of z)
Assume the problem is:
{{{ln((e^3*x^5)/(y^7*sqrt(z)))}}} = {{{ln(e^3*x^5)}}} - {{{ln(y^7*sqrt(z))}}}
However, we know that the ln of e^3 is 3 therefore we could write it
the square root can be written as an exponent of 1/2
{{{3 + ln(x^5)}}} - {{{7ln(y)}}}- {{{1/2}}}{{{ln(z)}}}