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Example 2: What is log 3 ( 58 ) log 3 ( 7 ).Here's another example using this method on a more difficult problem: X Research source If you're solving problems in math class, your teacher most likely expects you to leave the answer as a logarithm. You'll need a calculator if you need the answer for a practical purpose. ![]() Some logarithms are very difficult to solve by hand. Mhm.Leave the answer in logarithm form if you cannot simplify it. Okay, so therefore we see that X here equals three by two. So we can cancel out the common factors, Giving us the fractions three x 2. Okay, so this one is four times three and 80's 4 times two. All EnergyPlus models that have any electric power consumption are assumed to have a straightforward connection to utility grid service and no extra input is. And now the wedding both sides by eight we get x equals 12. So here we have the equation attacks -12 equals a zero At 12 to both sides. And this equals we have this toolkit cancel out. This equals And so this gives nine x minus eight Xs eight. #Condense logarithms with a power of fraction plus#And so this kills nine times of X -9 and this equals x plus three. So they cancel out giving us one X plus three in the right side. The next step we multiply both sides by X -1 is nine times of X -1 And this equals x plus three. ![]() So this kills three squared is nine, This equals x plus three. Now we convert this longer term to an exponential form And so this equals three face to the power of two and this equals X plus three. And so using this caution rules we can write this as a single longer term that there is a log of a by B which is X plus three Divided by B is X -1 To the base three. So here we consider the first to longer term expression S. And this equals a log of a by B to the basics. Truth that is a log A to the B C minus log B to the B. So first we write this as a single log rhythm for this. Here we have a log of express three to the base three minus log of x minus one to the base three equals two. I think for Tebow says we get e power three Plus four equals X. Is the expression inside the lock button that plays the X minus sport. ![]() So we write this as a E raised to the power of X. Using this conversion rule, that is a natural algorithm of M equals X. And so first let's convert this to its exponential form. This is already written as a single local term. Here we have a natural algorithm of the expression X -4 and this equals three. Now divide both sides by three And so 27 divided by three equals 9. We get 32 -5 is 27 and this equals three x. Let's play as a practice fight on both sides. And so to power five equals 32 And this equals three x. The base To provide this equal satu multiplied with itself by five times The span is so four. Go Live in Minutes A simple platform gives you the power to create and. #Condense logarithms with a power of fraction how to#Let's simplify and solve for X two raised to the power of five equals 32. Fractions Simplifier: How to simplify or reduce 15/20 to lowest terms or form. Is basically the expression three X plus five. That is two raised to the power of X equals five. And so when we use this exponential form we can rewrite this logarithms as B raised to the power of X. And the base is to hear And x equals five here. This expression inside the algorithm is M. So let's identify the MB and the Explorer here. Is the algorithm form Then the exponential form is B raised to the power of X equals M. ![]() So we are going to use this conversion rule which says that log in to the base B equals x. And so first we convert this lag rhythm to an exponential form and solve for X. And observed that this is already a single algorithm. So here we have a low growth um of the expression three X plus five To the base two equals 5. We now rewrite this as a single low growth. Solution for Condense the expression to the logarithm of a single quantity 1/2 log 4 ( x +1) +2log 4 ( x 1) +6log 4 x. ![]()
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