What would it be ?

Question

Evaluate loga (sqrt(a * x ^ - 7 * y ^ 7)) given that loga (x) = - 6.7 and loga (y) = 3.2

Answer 1

Unwrap log_a(ax^-7y⁷)^1/2 using logarithm rules:

1) log(xⁿ) = nlog(x)

and

2) log(xy) = log(x) + log(y)

first, pull the half exponent down to multiply log using equation 1

second, separate the products within the log into a sum of logs using equation 2

third, pull down the 7 and -7 exponents using equation 1

substitute for logx and logy and log_aa and evaluate.

Answer 2

log_a (ax^-7y⁷)^1/2 = log_a a^1/2 + log_ax^-7/2 + log_a y^7/2 = 1/2 log_a a -7/2 log_ax +7/2 log_a y

= 1/2 - 7/2(-6.7) +7/2(3.2) = 35.15