Calculus
Determine the validity of the given statement.
log8127=12log87\(\log\)_812^7=12\(\log\)_87
Evaluate the expression log232\(\log\)_232 without using a calculator.
If a constant d>1d>1 has a natural logarithm value of lnd≈5.2983\(\ln\) d\(\thickapprox\)5.2983, estimate the values of log5d\(\log\)_5d and logd5\(\log\)_{d}5 using the fact that ln5≈1.6094\(\ln\)5\(\thickapprox\)1.6094.
Given that loga(p)=0.45\(\log\)_{a}\(\left\)(p\(\right\))=0.45, evaluate the expression logap3\(\log\)_{a}p^3.