Convert the equation 42116 to logarithmic form Write Inx23 l

Convert the equation 4^-2=1/16 to logarithmic form. Write Inx+2/3 ln y-2 lnz as single log Find the domain of f(x)=log(5-x) Use the change of base formula to find log_3(Pi) in base 10. Which of the following is the Horizontal asymptote of f(x)=-3^x+2 Find the inverse function of f(X)=3^x+2. Solve the equation 2^x+2=16^x

Solution

1) 4^-2 = 1/16

y = log_b x is equivalent to b^y = x.

So, we can write : -2 = log₄(1/16)

Option c

2) lnx +(2/3)lny -2lnz

Use log property: logA -logB +logC = log(A/B)C

and logA^x = xlnA

lnx +lny^2/3 + lnz^-2

ln(xy^2/3/z^2)

Option a)

3 ) f(x) = log(5-x)

Domain: (5-x>0 )

x< 5

Option d

4) log3(pi)

loga(b) = logc(b)/logc(a)

log3(pi) = log10(pi)/log10(3)

option c