Functions with Base b
Key Questions

Log/Exp Inverse Properties
#b^{log_b x}=x# #log_b b^x=x# Other Log Properties
#log_b(xcdot y)=log_b x+log_b y# #log_b(x/y)=log_b xlog_b y# #log_b x^r=r log_b x#
I hope that this was helpful.

Answer:
#log_(a)(m^(n)) = n log_(a)(m)# Explanation:
Consider the logarithmic number
#log_(a)(m) = x# :#log_(a)(m) = x# Using the laws of logarithms:
#=> m = a^(x)# Let's raise both sides of the equation to
#n# th power:#=> m^(n) = (a^(x))^(n)# Using the laws of exponents:
#=> m^(n) = a^(xn)# Let's separate
#xn# from#a# :#=> log_(a)(m^(n)) = xn# Now, we know that
#log_(a)(m) = x# .Let's substitute this in for
#x# :#=> log_(a)(m^(n)) = n log_(a)(m)# 
Answer:
The reflection of the exponential function on the axis
#y=x# Explanation:
Logarithms are the inverse of an exponential function, so for
#y=a^x# , the log function would be#y=log_ax# .So, the log function tell you what power
#a# has to be raised to, to get#x# .Graph of
#lnx# :
graph{ln(x) [10, 10, 5, 5]}Graph of
#e^x# :
graph{e^x [10, 10, 5, 5]}