Question

Given that log10 3 = x and log10 7 = y, Express log 147 log 63 10 10 in terms of x and y.

Answer 1

To express log_147 63 in terms of x and y, use the properties of logarithms to rewrite the numbers as powers of 10 and then apply the property log_b(a^c) = c * log_b(a) to simplify the expression. The final result will be in terms of x and y.

Step-by-step explanation:

To express log147 63 in terms of x and y, we need to use the properties of logarithms. First, we can rewrite 147 and 63 as powers of 10 using the provided information:

147 = 32 * 71 = (10x)2 * (10y)1 = 102x * 10y

63 = 32 * 71 = (10x)2 * (10y)1 = 102x * 10y

Now, we can use the property of logarithms that logb(ac) = c * logb(a) to express log147 63 in terms of x and y:

log147 63 = log10(102x * 10y) = log10(102x + y) = 2x + y