Convert between exponential and logarithmic form

Learning Objectives Define the inverse relationship between exponential and logarithmic functions. Accurately identify the base, argument, and exponent in both exponential and logarithmic equations. Convert any given exponential equation into its equivalent logarithmic form. Convert any given logarithmic equation into its equivalent exponential form. Evaluate simple logarithmic expressions by first converting them to exponential form. Solve for a single variable in basic logarithmic equations by applying the conversion rule. Ever wonder how scientists measure the immense power of an earthquake or the acidity of a chemical solution? 🧪 It all comes down to the powerful relationship between exponents and logarithms! This tutorial focuses on the fundamental skill of converting...

TermDefinitionExample Exponential FormAn equation written in the form b^y = x, where a base 'b' is raised to an exponent 'y' to get a result 'x'.2^5 = 32 Logarithmic FormThe inverse of the exponential form, written as log_b(x) = y. It answers the question: 'To what exponent must we raise the base 'b' to get the argument 'x'?'log_2(32) = 5 Base (b)The number that is being raised to a power in exponential form, or the subscript in logarithmic form. The base must be a positive number not equal to 1 (b > 0, b ≠ 1).In both 2^5 = 32 and log_2(32) = 5, the base is 2. Exponent / Logarithm (y)In exponential form, it is the power to which the base is raised. In logarithmic form, it is the result of the logarithm.In both 2^5 = 32 and log...

The Fundamental Conversion Rule log_b(x) = y <=> b^y = x This is the core definition that connects logarithms and exponents. Use this rule to switch between the two forms. The conditions are b > 0, b ≠ 1, and x > 0. Logarithm of the Base Identity log_b(b) = 1 This follows from the conversion rule, because b^1 = b. The logarithm of a number that is the same as the base is always 1. Logarithm of One Identity log_b(1) = 0 This also follows from the conversion rule, because b^0 = 1. The logarithm of 1 is always 0 for any valid base.