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When the power is a variable and if it is a part of an equation, then it is called an exponential equation. We may need to use the connection between the exponents and logarithms to solve the exponential equations.
16 Νοε 2022 · In this section we will look at solving exponential equations and we will look at solving logarithm equations in the next section. There are two methods for solving exponential equations. One method is fairly simple but requires a very special form of the exponential equation.
To solve an exponential equation, take logs of both sides of the equation and bring the power down in front of the log. The resulting linear equation can be solved for x. For example, solve 5 x =13.
Now let us solve and practice the rule with a few examples. Solved Examples on Power of a Power Rule. 1. Identify the value of $(5^{2})^{2}$. Solution: Given expression: $(5^{2})^{2}$ The power of a power formula is, $(a^{m})^{n} = a^{mn}$ Let us multiply both the powers, $(5^{2})^{2} = 5^{2 × 2} = 5^{4}$ Now solve the expression. $5^{4} = 5 ...
To solve exponential equations without logarithms, you need to have equations with comparable exponential expressions on either side of the "equals" sign, so you can compare the powers and solve.
Laws of Exponents. Exponents are also called Powers or Indices. The exponent of a number says how many times to use the number in a multiplication. In this example: 82 = 8 × 8 = 64. In words: 8 2 could be called "8 to the second power", "8 to the power 2" or simply "8 squared". Try it yourself:
The power to the power rule states that 'If the base raised to a power is being raised to another power, then the two powers are multiplied and the base remains the same.'. The formula for the power of a power rule is (a m) n = a mn. Power of a power rule for negative exponents: (a -m) -n = a -m×-n = a mn.
