Solving Logarithmic and Exponential Equations

3^{2x – 6}  = 81

• x = log 4
• x = 5
• x = 4
• x = -1

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

2 * 4^{3x – 6} – 8 = 120

• x = 3
• x = 4
• x = 2.9
• x = 8

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

log₂(2) + log₂(8x) = 6

• x = 3
• x = 2
• x = 6
• x = 4

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

log₆(2x + 3) = 3

• x = 106.5
• x = 100
• x = 16
• x = 50

Tags

CCSS.HSF.BF.B.5

2log (2x)⁴ = 16

• x = 4
• x = 10
• x = 50
• x = 2

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.LE.A.4

log(4x)

• log4-logx

• log4+logx

• 4logx

• xlog4

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

log(xy²)

• logx+2logy

• logx+logy²

• logx-2logy

• logx+logy+log2

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Expand:  $\log_bmn$  

•  $\log_bm\ -\ \log_bn$  

•  $\log_bm+\log_bn$  

•  $m\log_bn$  

•  $n\log_bm$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Expand:  $\log_b\ \frac{m}{n}$  

•  $\log_bm\ -\log_bn$  

•  $\log_bm\ +\ \log_b\ n$  

•  $m\log_bn$  

•  $n\log_bn$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Expand:  $\log_b\ m^p$  

•  $\log_bm\ +\ \log_bp$  

•  $\log_bm-\log_bp$  

•  $\log_bp-\log_bm$  

•  $p\log_bm$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8