# Algebra II Solve! 10 POINTS!?

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

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.

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)

2)

ex / 2 = 5

ex / 2 = 5

Take logarithm to each side(base 10)

logex / 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.

edited Apr 27, 2013 by diane

3)

43x = 8

Take logarithm to each side

log43x = log8

3xlog4 = log23

3xlog22 = 3log2

Divide each side by 3

2xlog2 = log2

Divide each side by log2

2x = 1

x = 1 / 2.

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.