Express x in terms of a, b, and c

Express x in terms of a, b, and c :
1. Log x = 1/2 (3 log a + log b) - log c
2. Log x = (log a + log b + log c) / 2

1) Log x = 1/2 (3 log a + log b) - log c

log x= 3/2 log a +1/2 log b -log c

log x=log a^3/2+ log b^1/2 -log c

Use the logarithm rules


log x=log((a^3/2 * b^1/2)/c)

get rid of log

10^(log x)= 10^(log((a^3/2 * b^1/2)/c))

x=(a^3/2 * b^1/2)/c

2)Log x = (log a + log b + log c) / 2

log x=1/2 log a+ 1/2 log b+1/2 log c

log x=log a^1/2 + log b^1/2 +log c^1/2

Use the product rule

log x= log(a^1/2 * b^1/2 c^1/2)

log x= log ((abc)^1/2)

Get rid of log as above

10^(log x)=10^( log ((abc)^1/2))

x=(abc)^1/2 = sqrt(abc)

here's one way for #1

(use the properties for condensing logarithms...)

log x = 1/2 (3 log a + log b) - log c

=> log x = 1/2 (log a³ + log b) - log c

=> log x = 1/2 log (a³∙b) - log c

=> log x = log √(a³∙b) - log c

=> log x = log [√(a³∙b)/c]

=> x = √(a³∙b)/c

good luck