Solve Exponential and Log Equations

Tags

CCSS.HSF.LE.A.4

Tags

CCSS.HSF.BF.B.5

Tags

CCSS.HSF.LE.A.4

Tags

CCSS.HSF.BF.B.5

Solve:
log x + log 8 = 2 

• 10

• 12.5

• 15

• 17.5

Solve for a:

5^{a + 2} = 1/125

• -1

• -6/7

• -5

• 4

Answer explanation

If $125=5^3$ , then $\frac{1}{125}=5^{-3}$ $5^{\left(a+2\right)}=5^{-3}$

$\therefore\ \ \ \ a+2=-3$

log₂ x + log₂ (x + 5) = log₂ (3x + 8)

• x = 2

• x = -4

• x = 2 and x = -4

• no solution

log₂(x + 2) + log₂x  = 3

• -4, 2

• -2, 4

• 2 ;  -4 is extraneous

• 1 ;  -3 is extraneous