Question

Если log4 3=a,то log16 9=

Answer 1

                                     2
log₄3 = a, то log₁₆9 = ---log₄3 = a
                                     2

Answer 2

To find the value of log₁₆ 9 given that log₄ 3 = a, we can use the change of base formula for logarithms. The change of base formula states that for any positive numbers a, b, and c, the logarithm of c to the base a can be expressed in terms of logarithms to any other base b as follows:

logₐ c = log_b c / log_b a

In this case, we want to find log₁₆ 9, so we can use the change of base formula to express it in terms of logarithms to base 4:

log₁₆ 9 = log₄ 9 / log₄ 16

Now, we know that log₄ 3 = a, but we need log₄ 9. We can rewrite 9 as 3²:

log₄ 9 = log₄ (3²) = 2 log₄ 3

Substituting this into the equation:

log₁₆ 9 = (2 log₄ 3) / log₄ 16

Now, since log₄ 3 = a, we can substitute a into the equation:

log₁₆ 9 = (2a) / log₄ 16

The next step is to simplify the expression further. We know that 16 can be expressed as 4²:

log₁₆ 9 = (2a) / log₄ (4²)

Using the logarithmic property logₐ (b²) = 2 logₐ b:

log₁₆ 9 = (2a) / (2 log₄ 4)

Since log₄ 4 = 1, we have:

log₁₆ 9 = (2a) / (2 * 1) = 2a

Therefore, log₁₆ 9 simplifies to 2a.