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Pamela Kumar let us try to understand how to solve logarithmic equations we have two examples here log the base 4 of X minus 1 plus 1 equals 2 0 3 minus log to the base 3 of X plus 2 equals to 4 now to solve such equations we need to rearrange by that is the first step rearrange and the second step will be righted as exponential equalent right exponential equivalent so and then well solve right and then the solve for X so these are the steps involved let us begin with the very first equation which is log to the base 4 of X minus 1 plus 1 so lets rearrange take 1 to the right side so we get log to the base 4 of X minus 1 equals 2 minus 1 now second step is exponential equivalent so we know X minus 1 should be close to 4 to the power of minus 1 correct now what is 4 to the power of minus 1 X minus 1 is equals to 1 over 4 K that is what it is so X is equals to 1 over 4 plus 1 right which is you can take for common denominator 4 plus 1 is 5 to get 5 over 4 as your answer right 504 as

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The exponential function, exp : R (0,), is the inverse of the natural logarithm, that is, exp(x) = y x = ln(y). Remark: Since ln(1) = 0, then exp(0) = 1.

Typically we rearrange equations and formulas by using inverse operations to make one variable the subject of the formula. The subject of the formula is the single variable that is equal to everything else. i.e. the term by itself on one side of the equal sign.

Exponential transformation (inverse of log transformation)

We know that the inverse of a log function is an exponential. So, we know that the inverse of f(x) = log subb(x) is f^-1(y) = b^y. If the base is e and we are dealing with the natural log, then the inverse of f(x) = ln(x) is f^-1(y) = e^y.

0:51 3:14 Rearranging logarithmic equations into exponential equations - YouTube YouTube Start of suggested clip End of suggested clip So theres what this would look like written as an exponent just simply rearranging something thatsMoreSo theres what this would look like written as an exponent just simply rearranging something thats a logarithm into something that were more familiar with and thats an exponent or exponential.

Explanation: In order to eliminate the log based ten, we will need to raise both sides as the exponents using the base of ten. The ten and log based ten will cancel, leaving just the power on the left side. Change the negative exponent into a fraction on the right side.

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