How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log_(1/2) 15#?

Question

Elias Ackerman · Accepted Answer

I found: #-3.9# The Change of Base Formula tells you that: #log_ab=log_cb/log_ca# so that basically you changed the old base #a# into the new one #c#. In our case we can choose, as new base, the number #e# that gives us the natural log, #ln#, that it is possible to find with a pocket calculator. So: #log(1/2)15=ln15/ln(1/2)=-3.9#

Lincoln Anderson · Answer

undefined To evaluate the logarithm log_(1/2) 15 using the Change of Base Formula and a calculator, you can use the formula:

log_(a) b = log_(c) b / log_(c) a

where a, b, and c are positive real numbers and c is the desired base for the logarithm. In this case, we want to evaluate log_(1/2) 15, so we can rewrite this as:

log_(1/2) 15 = log(15) / log(1/2)

Now, use a calculator to evaluate the logarithms on the right side of the equation. Make sure your calculator is set to use base 10 logarithms (log) or natural logarithms (ln).

log(15) ≈ 1.1761
log(1/2) ≈ -0.3010

Now, plug these values back into the formula:

log_(1/2) 15 ≈ 1.1761 / -0.3010 ≈ -3.9080

Therefore, log_(1/2) 15 ≈ -3.9080.