Can a logarithmic equation have no solution?
Can a logarithmic equation have no solution?
1 Expert Answer Since the argument of the log is negative, there is no solution.
What is the difference between logarithmic equations and exponential equations?
An exponential equation is an equation in which the variable appears in an exponent. A logarithmic equation is an equation that involves the logarithm of an expression containing a variable. To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number.
What is logarithmic equation with example?
| LOGARITHMIC EQUATIONS | ||
|---|---|---|
| Examples | EXAMPLES OF LOGARITHMIC EQUATIONS | |
| Log2 x = -5 | 5 + ln 2x = 4 | |
| ln x + ln (x – 2) = 1 | log6 x + log6 (x + 1) = 1 | |
| Solving | STEPS TO SOLVE A logarithmic EQUATIONS |
What are the example of logarithmic inequalities?
The argument of a logarithm must be positive! Thus, it is also necessary to take into account any inequalities resulting from the arguments being positive; for example, an inequality involving the term log 2 ( 2 x − 3 ) \log_2 (2x-3) log2(2x−3) immediately requires x > 3 2 x>\frac{3}{2} x>23.
How to write a logarithmic equation?
The logarithmic function, y = log b ( x) , can be shifted k units vertically and h units horizontally with the equation y = log b ( x + h) + k . If k > 0 , the graph would be shifted upwards.
How would I solve this logarithmic equation?
SOLVING LOGARITHMIC EQUATIONS 1. Example 1: Solve for x in the equation Ln ( x )=8. Check: Step 1: Let both sides be exponents of the base e. Example 2: You can check your answer in two ways. Check: Solve for x in the equation 7 Log (3 x )=15. Example 3: Step 1: Isolate the logarithmic term before you convert the logarithmic equation to an exponential equation.
How to calculate log2?
Formula: Log base 2 of a number “n” is the power to which the number “2” (base value) must be raised to obtain the value n. Hence, log2 calculation can be done using the below formula Log2 n = 2x = n
How do you solve an exponential equation using log?
Exponential equations can be solved by taking the log of both sides. Steps: 1) As much as possible, get the log by itself. 2) Take the log (or natural log) of both sides. 3) Simplify as needed using the log rules. 4) Solve the equation for the variable.