Question

Given that log2=a;log3=b and log5=c, find an expression for log81²-log75+log243+2log45-log32 in terms of a, b, c. ​ A) 2a+3b+2c

B) 2a−3b+2c
C) 2a+3b−2c
D) 2a−3b−2c

Answer 1

The expression log81²-log75+log243+2log45-log32 in terms of a, b, and c is -3a + 8b.

Step-by-step explanation:

To find an expression for log81²-log75+log243+2log45-log32 in terms of a, b, and c, we need to use the properties of logarithms.

First, let's rewrite the expression using the properties of logarithms:

log81²-log75+log243+2log45-log32

= 2log81 - log75 + log243 + 2log45 - log32

Now, we can substitute the given values a = log2, b = log3, and c = log5 into the expression:

= 2(a) - (b) + log(3^5) + 2log(3^2) - log(2^5)

= 2a - b + 5b + 2(2b) - 5a

Simplifying further, we obtain:

2a - b + 5b + 4b - 5a

= -3a + 8b

Therefore, the expression log81²-log75+log243+2log45-log32 in terms of a, b, and c is -3a + 8b.