Question

4^(log4 5)+log7 2-log7 14

Answer 1

5+log₇(2/14) = 5 + log₇(1/7) = 5 - 1 =4

Answer 2

To simplify the expression 4^(log4 5) + log7 2 - log7 14, we can break it down step by step.

1. Use the property that 4^(log4 5) is equal to 5. This is because the base of the logarithm (4) matches the base of the exponent (4), so the two operations cancel each other out. So, the expression becomes: 5 + log7 2 - log7 14

2. Logarithms can be used to combine or separate exponents, so you can rewrite log7 14 as log7 (2 * 7). Now, the expression is: 5 + log7 2 - (log7 2 + log7 7)

3. Logarithms also have the property that log(a * b) = log(a) + log(b). Apply this property to log7 (2 * 7): 5 + log7 2 - (log7 2 + log7 7) = 5 + log7 2 - log7 2 - log7 7

4. Finally, since we have log7 2 - log7 2, they cancel each other out: 5 + 0 - log7 7

5. Simplify further by removing the 0: 5 - log7 7

So, the simplified expression is 5 - log7 7.