Find the numerical value of the log expression.
log a=4 log b=9 log c=4
log b^7/a^3c^2
Using logarithmic properties, we can rewrite the expression as:
log b^7/a^3c^2 = log (b^7) - log (a^3) - log (c^2)
Now substitute the given values:
= 7 log b - 3 log a - 2 log c
= 7(9) - 3(4) - 2(4)
= 63 - 12 - 8
= 43
Therefore, the numerical value of the log expression is 43.
To find the numerical value of the log expression log b^7/a^3c^2, we can use the properties of logarithms.
Step 1: Rewrite the expression using the properties of logarithms:
log b^7/a^3c^2 = log (b^7) - log (a^3c^2)
Step 2: Substitute the given values of log a, log b, and log c:
log (b^7) - log (a^3c^2) = 7 log b - (3 log a + 2 log c)
Step 3: Substitute the given numerical values of log a, log b, and log c:
7 log b - (3 log a + 2 log c) = 7 * 9 - (3 * 4 + 2 * 4)
Step 4: Simplify the expression:
7 * 9 - (3 * 4 + 2 * 4) = 63 - (12 + 8) = 63 - 20 = 43
Therefore, the numerical value of the log expression log b^7/a^3c^2 is 43.
To find the numerical value of the log expression, we can use logarithmic properties.
First, let's rewrite the log expression using the properties:
log b^7/a^3c^2 = log (b^7) - log (a^3c^2)
Next, substitute the given values of log a, log b, and log c:
= (9) - (4^3) - (4^2)
Then, simplify the equation:
= 9 - 64 - 16
= -71
Therefore, the numerical value of the log expression log b^7/a^3c^2 is -71.