Question

Answer the questions.
a. Solve the logarithmic equations.
1. log4 64 =m
2. log8 n =3
3. logp 4096= 3
4. log32 q =3

b. Study the pattern in the equations. Use your observations to solve the equation for a. Express your answer in terms of x.

log4^x 2^a = 3

Answer 1

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem A1

$log_464=m$

$\frac{log(64)}{log(4)}=m$

$3=m$

Problem A2

$log_8n=3$

$n=8^3$

$n=512$

Problem A3

$log_p4096=3$

$4096=p^3$

$16=p$

Problem A4

$log_{32}q=3$

$q=32^3$

$q=32768$

Problem B

$log_{4^x}2^a=3$

$2^a=(4^x)^3$

$2^a=4^{3x}$

$2^a=(2^2)^{3x}$

$2^a=2^{6x}$

$a=6x$

$\frac{a}{6}=x$