Logarithm-- Inverse of an Exponential Function
The logarithm serves as the inverse operation of an exponential function, offering a crucial tool in various mathematical contexts. As the antithesis to exponential growth, logarithms provide a means to determine the power to which a base must be raised to yield a given number. This fundamental relationship between logarithms and exponentials underpins their utility in fields ranging from finance to physics, facilitating the comprehension and manipulation of data exhibiting exponential behavior. Understanding the concept of logarithms is essential for navigating complex mathematical models and solving equations involving exponential quantities.
Questions
- If #2^x xx4^(x+1)=8# what is the value of #x#?
- What is the inverse function of #f(x) = -1/2x -3#?
- How do you evaluate #log_14 (1/14)#?
- How do you write the exponential notation for #log_2 16 = x#?
- How do you evaluate #10 log18 - log3#?
- How do you solve #3 * 5^(x-1) + 5^x = 0.32#?
- How do you write #10^3 = 1000# in log form?
- What is the logarithm of .0856?
- How do you solve #8ln(x) = 1#?
- What is the domain, range, intercept, and vertical asymptote of #f(x) = log(x-2)#?
- How do you find the value of x: #log_x (121/289) = 2#?
- How do you evaluate #log_2 4 - log_2 16#?
- How do you write #log_3 243=5# in exponential form?
- How do you evaluate #log_125 (1/5)#?
- If #log_ba=1/x and log_a √b =3x^2#, show that x =1/6?
- How do you solve #log_5x + log_3 x=1#?
- If #y# varies inversely as #x# and #y =40# when #x = 5#, what is the constant?
- How do you write #log100=2# in exponential form?
- How do you evaluate #log_(1/4) (1/4)#?
- How do you solve #2log_6 4-1/4log_6 16=log_6 x#?