5. Log[9](x+4)+log[9](x-4)=1 calculate

6. Log[3](3) raised to the (4x-1)=15 Calculate

7. 4 raised to (2x-3)=9 raised to (x+3) Calculate

5.

log[9](x + 4) + log[9](x - 4) = 1

Recall : Logarithm formula loga + logb = logab

logg[9](x + 4)× [9](x - 4) = 1

log92(x + 4)(x - 4) = 1

Recall : (a + b)(a - b) = a2 - b2

log81(x2 - 16) = 1

Remove logarithm

81(x2 - 16) = 101

x2 - 16 = 10 / 81

x 2 = (10 / 81) + 16 = 1306 / 81

x = 4.01

6.

log[3](3)4x - 1 = 15

Recall : Logarithm formula logab = loga + logb

log[3] + log(3)4x - 1 = 15

(4x - 1)log(3) = 15 - 0.4771

(4x - 1)log3 = 14.5229

4x - 1 = 14.5229 / 0.4771

4x - 1 = 30.43995

4x = 31.43995

x = 31.43995 / 4

x = 7.8599875

7.

42x - 3 = 9x + 3

Take logarithm to each side

log42x - 3 = log9x + 3

Recall : logarithm formula logxn = nlogx

(2x - 3)log4 = (x + 3)log9

2(2x - 3)log2 = 2(x + 3)log3

(2x - 3)log2 = (x + 3)log3

2x log2 - 3log2 = xlog3 + 3log3

2xlog2 - xlog3 = 3(log3 + log2)

x(2log2 - log3) = 3(0.4771 + 0.3010)

x(0.6020 - 0.4771) = 3(0.7781)

x ( 0.1249) = 3(0.7781)

x = 3(0.7781) / (0.1249)

x  =  3(6.2298) = 18.6894