2log3+4log2-3

Answer 1

To solve this expression, we need to use the properties of logarithms.

First, we can apply the power rule of logarithms, which states that log_b(x^a) = alog_b(x). Using this rule, we can rewrite the expression as:

2log3 + 4log2 - 3 = log3^2 + log2^4 - log3^3

Next, we can apply the product rule of logarithms, which states that log_b(xy) = log_b(x) + log_b(y). Using this rule, we can simplify the expression further:

log3^2 + log2^4 - log3^3 = log3^2 + log2^4 - log(3^3)

Now, we can use the power rule of logarithms again to simplify:

log3^2 + log2^4 - log(3^3) = log9 + log16 - log27

Finally, we can use the addition/subtraction rule of logarithms, which states that log_b(x) ± log_b(y) = log_b(x*y). Using this rule, we can simplify the expression one last time:

log9 + log16 - log27 = log(9 * 16) - log27

Now, we can calculate the final value:

log(9 * 16) - log27 = log(144) - log27

Using logarithmic identities, we can simplify further:

log(144) - log27 = log(144/27)

Now, we can simplify the division:

log(144/27) = log(144) - log(27)

Using a calculator to calculate the logarithms of 144 and 27, we get:

log(144) ≈ 2.158
log(27) ≈ 1.431

Therefore, the final value of the expression is approximately:

2.158 - 1.431 ≈ 0.727