 # Exponential and logarithmic functions in carbon 14 dating when dating someone whos separated

$$2^=2^$$ To take a power of a power, multiply exponents.$$3x 6=4x 4$$ Use the one-to-one property to set the exponents equal. Example $$\Page Index$$: Solving Equations by Rewriting Roots with Fractional Exponents to Have a Common Base Solve $$2^=\sqrt$$. Sometimes the terms of an exponential equation cannot be rewritten with a common base.We can use this fact, along with the rules of logarithms, to solve logarithmic equations where the argument is an algebraic expression. Figure $$\Page Index$$ represents the graph of the equation.For example, consider the equation $$_2(2) _2(3x−5)=3$$. On the graph, the 0\) and any positive real number $$b$$, where $$b≠1$$, $$_b S=_b T$$ if and only if $$S=T$$. So, if $$x−1=8$$, then we can solve for $$x$$,and we get $$x=9$$.

$$8=2x−10$$ Apply the one-to-one property of exponents. Solution: $$8^=^$$ $$^=^$$ Write $$8$$ and $$16$$ as powers of $$2$$.

$$e^−e^x=56$$ $$e^−e^x−56=0$$ Get one side of the equation equal to zero. $$e^x 7=0$$ or $$e^x−8=0$$ If a product is zero, then one factor must be zero. $$e^x=8$$ Reject the equation in which the power equals a negative number.

$$x=\ln8$$ Solve the equation in which the power equals a positive number.

Solution: $$2^=2^$$ Write the square root of $$2$$ as a power of $$2$$. In these cases, we solve by taking the logarithm of each side.

Recall, since $$\log(a)=\log(b)$$ is equivalent to $$a=b$$, we may apply logarithms with the same base on both sides of an exponential equation. $$x\ln5−x\ln4=−2\ln5$$ Get terms containing $$x$$ on one side, terms without $$x$$ on the other. One common type of exponential equations are those with base $$e$$. 