Evgeny.Makarov said:By definition of logarithm, $\log_{16}x$ is the number $a$ such that $16^a=x$. Note that $16^a=(4^2)^a=4^{2a}$. Therefore, if $\log_{16}x=a$, then $\log_4x=2a=2\log_{16}x$.
Do you know what "log_16" means? In particular, do you know that, for any positive x, if y= log_16(x) then x= 16^y? Of course 16= 4^2 so x= (4^2)^y= 4^(2y).RTCNTC said:Solve the log equation
log_16 (3x-1)=log_4 (3x) + log_4 (0.5)
Can someone get me started?
The left side has base 16 and the right side base 4.
How is this done when two different bases are involved?
A log equation is a mathematical expression that involves the logarithm function. It is written in the form of logb(x) where b is the base and x is the argument. It is used to solve for the exponent in exponential equations.
To solve a log equation, you must first isolate the logarithmic term on one side of the equation. Then, you can rewrite the equation in exponential form and solve for the unknown variable. Make sure to check your solution by plugging it back into the original equation.
The properties of log equations include the product rule, quotient rule, power rule, and change of base rule. These properties allow you to manipulate log equations to solve for unknown variables or simplify complex expressions.
The natural log, written as ln(x), has a base of e (approximately 2.718). The common log, written as log(x), has a base of 10. This means that ln(x) is the inverse of ex and log(x) is the inverse of 10x.
Log equations are used in many fields such as finance, science, and engineering. They can be used to model growth or decay, calculate interest rates, and measure the loudness of sound. They are also used in data analysis to convert numbers that vary over a large range into a more manageable scale.