# Imdma re write as a logarithmic equation

Site Navigation Properties of Logarithms Logarithmic functions and exponential functions are connected to one another in that they are inverses of each other. You may recall that when two functions are inverses of each other, the x and y coordinates are swapped. Raise both sides of the equation by the power that undoes the root. Result of cubing both sides. Solve the resulting linear equation. If you raise both sides to an even power you need to check for extraneous solutions.

Answer written as a solution set. Solve Our first task is to recognize what type of equation we have. It has a variable expression in the exponent position, so this is an exponential type of equation. Next, we apply the procedures that we learned for solving such types as shown in the table below. Current written form of equation. Our first instinct with exponential types is to try and rewrite both exponential expressions in the same base. Here I could rewrite nine as three squared.

Use the power-to-power exponent rule to multiply the exponents. I multiplied the exponents. The one-to-one property of exponential expressions allows us to equate the exponents. I solved the resulting quadratic equation using our previously reviewed techniques.

Be sure to check your answers. There is an alternative style that you could use at one point in the above process. Here is that alternative. I divided both sides by. I applied the quotient rule of exponents. I cleaned up the exponent. I rewrote the exponential equation in a logarithmic form, which is the style of solving an exponential equation when you isolate the exponential expression on one side against a constant on the other.

This style has more of the flow that I described in the general approach to solving equations. That is to combine expressions together to form one expression against a constant, and then undo what is being done to the variable. This is one of the logarithmic properties.

The rest of the process is now the same as we did above.The idea is that if we can get a single logarithmic expression on one side against a constant on the other, we can then rewrite the equation as an exponential type.

This is the basic strategy for solving logarithmic equations. We will rewrite the log equation exponentially using the definition of logs to help us get the x outside of the log. If you need a review on the definition of log functions, feel free to go to Tutorial Logarithmic .

Exponential and Logarithmic Functions Practice Test 1. The population of a pod of bottlenose dolphins is modeled by the function $A\left(t\right)=8{\left(\right)}^{t}$, where t is given in years. ©s Z2U0\1h6A jKtuHtdaT JS\ovfMtnwkafrKeA CLzLzCu.P w LAZlPlJ TrpiZgjhatosY TrleNsXeKrYvCeOdo.n W BMzandYe[ jw`iWtkhp gIfnmfgivniiAtCeG qPirYeOcmaLlacuuhlyussx.

## Related questions

Logarithmic and Exponential Equations OBJECTIVES 1. Solve a logarithmic equation 2. Solve an exponential equation 3.

Rewrite the original equation as log 5 2 Now, x 50 x 2 25 x 2 52 x 2 NOTE Because no base is written, it is assumed to be NOTE Given the . (Thomason – Fall ) MATH – College Algebra – Logarithms Definition: Let b be any positive number other than 1 and let x be any positive number.

Then by definition, the logarithm to the base b of x, denoted logbx, is the number that can be used as an.

Convert Logarithms and Exponentials