Visually solve 15-20 logarithm questions on basic properties with jee advanced teachers approach. The visuals should look like handwritten math and use all handwritten techniques ( putting cut mark when cancelling something )

视频信息

答案文本 复制

视频字幕 复制

Let's solve our first logarithm problem. We need to simplify log base 2 of 8. First, we recognize that 8 equals 2 to the power of 3. Using the power rule of logarithms, we get 3 times log base 2 of 2. Since log base 2 of 2 equals 1, we cross it out and replace with 1. Therefore, our answer is 3. Now let's solve log base 3 of 9 plus log base 3 of 27. First, we rewrite 9 as 3 squared and 27 as 3 cubed. Using the power rule, we get 2 times log base 3 of 3 plus 3 times log base 3 of 3. Since log base 3 of 3 equals 1, we cross out these terms and replace with 1. This gives us 2 plus 3, which equals 5. Let's solve log base 2 of 32 minus log base 2 of 4. Using the quotient rule of logarithms, this becomes log base 2 of 32 divided by 4, which equals log base 2 of 8. We can rewrite 8 as 2 to the power of 3. Using the power rule, we get 3 times log base 2 of 2. Since log base 2 of 2 equals 1, we cross it out and our answer is 3. Let's solve log base 4 of 8. We can rewrite this as log base 2 squared of 2 cubed. Using the change of base property for powers, this becomes 3 over 2 times log base 2 of 2. Since log base 2 of 2 equals 1, we cross it out and our answer is 3 over 2. Let's solve log base 3 of 5 times log base 5 of 3. Using the reciprocal property of logarithms, log base 5 of 3 equals 1 over log base 3 of 5. So we have log base 3 of 5 times 1 over log base 3 of 5. We can cross out the log base 3 of 5 terms in the numerator and denominator, giving us 1.