Find the exact value of each expression(a) log2 64(b) log6136(c) log8 2(d) ln e√22. Find the exact value of each expression(a) log10 1.25 + log10 80(b) log5 10 + log5 20 − 3 log5 23. Find the exact value of each expression(a) 2(log2 3+log2 5)(b) e3 ln 2

Find the exact value of each expression (a) log2 64: This is asking 2 to what power equals 64. The answer is 6 because 2^6 = 64. (b) log6 136: This is asking 6 to what power equals 136. There is no exact integer value for this, so it would be a decimal or fraction. (c) log8 2: This is asking 8 to what power equals 2. The answer is 1/3 because 8^(1/3) = 2. (d) ln e√2: This is asking e to what power equals √2. The natural logarithm of e to any power is just that power, so the answer is √2.

Find the exact value of each expression (a) log10 1.25 + log10 80: This is the same as log10 (1.2580) because of the rule logb(mn) = logb(m) + logb(n). So, log10 100 = 2. (b) log5 10 + log5 20 − 3 log5 2: This is the same as log5 (1020/2^3) = log5 5 = 1.

Find the exact value of each expression (a) 2(log2 3+log2 5): This is the same as 2 log2 (35) = 2 log2 15. There is no exact integer value for this, so it would be a decimal or fraction. (b) e3 ln 2: This is the same as e^(3ln(2)). The base e and the natural logarithm ln cancel each other out, so the answer is 2^3 = 8.