Find The Inverse -2 Natural Log Of X+1 - Mathway

Enter a problem... Algebra Examples Popular Problems Algebra Find the Inverse -2 natural log of x+1 Step 1Interchange the variables.Step 2Solve for .Tap for more steps...Step 2.1Rewrite the equation as .Step 2.2Divide each term in by and simplify.Tap for more steps...Step 2.2.1Divide each term in by .Step 2.2.2Simplify the left side.Tap for more steps...Step 2.2.2.1Cancel the common factor of .Tap for more steps...Step 2.2.2.1.1Cancel the common factor.Step 2.2.2.1.2Divide by .Step 2.2.3Simplify the right side.Tap for more steps...Step 2.2.3.1Move the negative in front of the fraction.Step 2.3To solve for , rewrite the equation using properties of logarithms.Step 2.4Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .Step 2.5Solve for .Tap for more steps...Step 2.5.1Rewrite the equation as .Step 2.5.2Subtract from both sides of the equation.Step 3Replace with to show the final answer.Step 4Verify if is the inverse of .Tap for more steps...Step 4.1To verify the inverse, check if and .Step 4.2Evaluate .Tap for more steps...Step 4.2.1Set up the composite result function.Step 4.2.2Evaluate by substituting in the value of into .Step 4.2.3Simplify each term.Tap for more steps...Step 4.2.3.1Cancel the common factor of and .Tap for more steps...Step 4.2.3.1.1Factor out of .Step 4.2.3.1.2Cancel the common factors.Tap for more steps...Step 4.2.3.1.2.1Factor out of .Step 4.2.3.1.2.2Cancel the common factor.Step 4.2.3.1.2.3Rewrite the expression.Step 4.2.3.1.2.4Divide by .Step 4.2.3.2Multiply .Tap for more steps...Step 4.2.3.2.1Multiply by .Step 4.2.3.2.2Multiply by .Step 4.2.3.3Exponentiation and log are inverse functions.Step 4.2.4Combine the opposite terms in .Tap for more steps...Step 4.2.4.1Subtract from .Step 4.2.4.2Add and .Step 4.3Evaluate .Tap for more steps...Step 4.3.1Set up the composite result function.Step 4.3.2Evaluate by substituting in the value of into .Step 4.3.3Combine the opposite terms in .Tap for more steps...Step 4.3.3.1Add and .Step 4.3.3.2Add and .Step 4.3.4Use logarithm rules to move out of the exponent.Step 4.3.5The natural logarithm of is .Step 4.3.6Multiply by .Step 4.3.7Cancel the common factor of .Tap for more steps...Step 4.3.7.1Move the leading negative in into the numerator.Step 4.3.7.2Factor out of .Step 4.3.7.3Cancel the common factor.Step 4.3.7.4Rewrite the expression.Step 4.3.8Multiply.Tap for more steps...Step 4.3.8.1Multiply by .Step 4.3.8.2Multiply by .Step 4.4Since and , then is the inverse of .

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