Algebra II Solve! 10 POINTS!?

Question

1) cube root 8√ 7x+4 = cube root 8√ 2x+9

2) e^x / 2 = 5

3) 4^3x = 8

4) -2 + 5log x + 8

Answer 1

1)

cube root 8√7x + 4 = cube root 8√2x + 9

Take cube to each side

8√7x + 4 = 8 √2x + 9

√7x + 4 = √2x + 9

Take square to each side

7x + 4 = 2x + 9

5x = 5

x = 1.

Answer 2

2)

e^x / 2 = 5

Multiply each side by 2

e^x = 10

Take logarithm to each side(base 10)

loge^x = log10

x loge = log10

x loge = 1

Divide each side by loge

x = 1 / loge

x = 1 / 0.4343

x = 2.3025(approximately)

Answer 3

2)

e^{x / 2} = 5

e^{x / 2} = 5

Take logarithm to each side(base 10)

loge^{x / 2} = log5

(x / 2) loge = log5

(x /2)0.4343 = 0.69897

(x / 2) = 0.69897 / 0.4343

x / 2 = 1.6094

x = 3.2188.

 

Answer 4

3)

4^3x = 8

Take logarithm to each side

log4^3x = log8

3xlog4 = log2³

3xlog2² = 3log2

Divide each side by 3

2xlog2 = log2

Divide each side by log2

2x = 1

x = 1 / 2.

Answer 5

4)

-2 + 5logx + 8 = 0

5logx + 6 = 0

Subtract 6 from each side

5logx = -6

logx⁵ = -6

Remove log to left side

x⁵ = 10^-6

Apply the power rule

x = 10^-6/5.