I really need help with these three!

Question

Calculate log3 100 (where log3 means log to the base 3). Rewrite as a logarithm to the base 2. 

log3 100 = 4.1918 = log2 18.2750 
log3 100 = 4.6416 = log2 24.9609 
log3 100 = 3.3333 = log2 10.0791 
log3 100 = 0.2386 = log2 1.1798 
log3 100 = 4.1918 = log2 2.0474 



Calculate log2 64 (where log2 means log to the base 2). Rewrite as a logarithm to the base 8. 

log2 64 = 6 = log8 262144 
log2 64 = 6 = log8 48 
log2 64 = 6 = log8 1.5 
log2 64 = 1.8062 = log8 42.7722 
log2 64 = 1.6667 = log8 32.0032 



Calculate log5 42 (where log5 means log to the base 5). Rewrite as a logarithm to the base 8. 

log5 42 = 0.4306 = log8 2.4483 
log5 42 = 2.3223 = log 210.0390 
log5 42 = 0.4306 = log8 3.4448 
log5 42 = 2.3223 = log8 18.5784 
log5 42 = 2.3223 = log8 125.0967

Answer 1

log_ab = log b / log a               conversion of base 

 

log₃100 = log 100 / log 3

log₃100 ≈ 2 / 0.477121255

 

The same process is done for the remainder.

Answer 2

Ok, so

log₃ 100 is asking you "3 to what power gives you 100".  You can estimate it since

3³ = 27

3⁴= 81

3⁵=243

 

So you know it will be somewhere between 4 and 5, but solving the exact value manually is difficult, if not impossible.  You will want to use a scientific calculator to solve.  Once you have the answer, in this case

4.1918

 

you then want to take this value so that

2^4.1918 = x where x will be the log₂ value.  Again you will want to use a calculator and you will get 18.2750 which means the first answer is correct.

 

Use this and you will get the next two in the same fashion.