log4 g log4 9 log 4 5 log67s2 112 log670s Solve for x in

log4 g + log4 9 = log 4 5 log6(7s^2 + 112) = log6(-70s) Solve for x in terms of y: y = log_4(-3x^5) y = log_2(9x^3 - 10)

Solution

5)

log₄ g + log₄ 9 = log₄ 5

log₄ (g * 9) = log₄5                     // log_a x + log_a y = log_a (x*y)

log g / log 4      + log 9 / log 4 = log 5 / log 4

(log 9 + log 9) / log 4 = log 5 / log 4

Taking antilog borh sides, we get

9 * g = 5

g = 5/9

.

6)

log₆ (7s² + 112) = log₆ (-70s)

log (7s² + 112) / log 6 = log (-70s) / log 6

taking antilog both sides, we get

7s² + 112 = -70s

7s² + 70s + 112 = 0

s² + 10s + 16 = 0

s² + 8s + 2s + 16 = 0

s(s+8) + 2(s+8) = 0

(s+8) (s+2) = 0

s = -2 or s = -8

.

7)

y = log₄ (-3x⁵)

Using   log _b x = y = > x = b^y

so using this we get

(-3x⁵) = 4^y

x⁵ = 4^y / 3

x = (4^y / 3)^1/5