Can a logarithmic equation have no solution?

If we were to solve for x by applying the rules and properties of logs, then plug in those x values into the original equation, then the equation should be satisfied. Also, note that the argument of the log after plugging in the x values must be positive. Since the argument of the log is negative, there is no solution.

How do you solve logarithmic unknown equations?

The procedure of solving equations with logarithms on both sides of the equal sign.

  1. If the logarithms have are a common base, simplify the problem and then rewrite it without logarithms.
  2. Simplify by collecting like terms and solve for the variable in the equation.

How do you translate logarithmic equations?

The logarithmic function, y=logb(x) , can be shifted k units vertically and h units horizontally with the equation y=logb(x+h)+k . If k>0 , the graph would be shifted upwards. If k<0 , the graph would be shifted downwards. If h>0 , the graph would be shifted left.

Which of the logarithmic equation is not possible?

Therefore log 5-7 is the one which is not possible in logarithmic expressions.

Which logarithms do not exist?

Why log (-1) does not exist – Method 1. You can’t take the logarithm of a negative number or of zero. The logarithm of a positive number may be positive or zero. Log or ln is only defined for x that are strictly greater than 0.

What if there is no base in a log?

If a log has no base written, you should generally (in algebra classes) assume that the base is 10. The other important log is the “natural”, or base-e, log, denoted as “ln(x)” and usually pronounced as “ell-enn-of-x”.

How do you convert e to LN?

The natural log simply lets people reading the problem know that you’re taking the logarithm, with a base of e, of a number. So ln(x) = loge(x). As an example, ln(5) = loge(5) = 1.609.

How do you eliminate a log?

To rid an equation of logarithms, raise both sides to the same exponent as the base of the logarithms.