Solve the following: Leave answers in exact form. No decimals!!! a. 8(5)x + 2 = 26 b. 2=log (x+1) 5

Question

(x+1) is the base of the log

Answer 1

8(5^x) + 2 = 26

8(5^x) = 24

5^x = 3

x = log₅3, or equivalently, log3 / log5 or ln3 / ln5

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log_x+15 = 2

(x+1)² = 5

x+1 = ±√5

x+1 can't be -√5 since the base of a logarithm can't be negative

So, x = -1 + √5

Answer 2

a)

8(5)^x +2 = 26

5^x= 4

x = ln(4)/ln(5)

b)

2 = log_x+15

(x+1)² = 5

x+1 = ±√5

x = ±√5-1