Numerous understudies view logarithms as a wellspring of disarray, however with just enough practice and comprehension of the standards, tackling log conditions need not be essentially as troublesome as it might show up. To outline this strategy, we will stroll through tackling a condition like log2x = log53 + 1, where x is the variable we are addressing.
Graphing logarithmic functions, which can provide a visual representation of the relationships that exist between various variables, makes it easier to comprehend and solve log equations. Using the properties of logarithms and plotting the given logarithmic capabilities on a chart, we can solve log2x = log53 + 1 by graphing. round to the nearest tenth. You will develop a methodical approach to tackling similar log questions in the future.
Solving the Question Step by Step
Here is the complete guide on solving the log question step by step:
Recognizing the Issue
Understanding what the equation is telling us is the first step. In log structure, log2x = log53 + 1, we have a logarithm with base 2 on the left side and an amount of a logarithm on the right side. We want to tackle for x.
Recall that in an outstanding structure, the base turns into the foundation of the example and the outcome is the type. Hence, 2(log2x) = 2(log53 + 1) equals to log2x = log53 + 1.
Graphing the Exponential Function
Let’s plot the exponential function y = 2x now that we have the equation in exponential form. This diagram will assist us with envisioning where the different sides of the situation cross. To find the convergence point between the remarkable capability and the line y = log53 + 1, we can set the two capabilities equivalent to one another. In this way, we have 2^x = 53 + 1.
Simplifying the Equation
Improve on the situation 2^x = 53 + 1 to 2^x = 54. Now, we must use the logs of both sides to solve for x. By taking the log base 2 of the two sides, we get log2(2^x) = log2(54), which rearranges to x = log2(54).
Getting Close to the Solution
We can estimate log 2(54) to be around 5.77 using a calculator. To check our answer, we can substitute x = 5.77 back into the first condition log2x = log53 + 1. When we do this, we discover that log2(5.77) roughly corresponds to log53 + 1.
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Final Lines
Log questions like log2x = log53 + 1 can be solved using graphing, which is a helpful tool. You can easily solve the equation and determine the value of x by following these step-by-step instructions. Make sure to focus on the slant and catch of the lines to find the arrangement precisely. You will be able to confidently answer log questions with practice and patience.
