Question

Solve each exponential equation. Give answers as decimals accurate to the thousands place.

1) log(base5)14=2x-9

2) log(base7)5=7-6x

3) (1/3)^(3x+5)=(9)^(8-x)

4) 4^(x-5)=8^(x+2)

Answer 1

so did you try?

Answer 2

i tried 3 and 4 but im not sure if its correct

3) -21
4) -16

and im not sure how to do 1 and 2

Answer 3

1) for example:

log5 (14) = 2x-9

5^[log5 (14)] = 14 = 5^(2x-9)

so the question is
5 to the what = 14 ?
say 5^z = 14 (we know that z is (2x-9))

z log 5 = log 14 using base 10 logs (or e or whatever, I use base 10)
z = log14/log5 = 1.146 / .699 = 1.64
so
2x-9 = 1.64
2x = 10.64
x = 5.32

Answer 4

try 3)

(1/3)^(3x+5)=(9)^(8-x)

(3x+5) log .333333333 = (8-x) log 9

(3x+5)(-.4771) = (8-x) (.9542)

(3x+5) = (x-8) 2 that was lucky :)

3 x + 5 = 2x-16

x = -21 agree
=====================
or this way
(1/3)^(3x+5)=(9)^(8-x)

1^(3x+5)/3^(3x+5) = 3^(16-2x)

1 = 3^(x+21)
x+21 = 0
x = -21

Answer 5

4) 4^(x-5)=8^(x+2)

(2^2)^(x-5) = (2^3)^(x+2)

2^(2x-10) = 2^(3x+6)

2x-10 = 3x+6

x = -16 agree

Answer 6

2) log(base7)5=7-6x

5 = 7^(7-6x) = 7^z

log 5 = z log 7

z = .827

7 - 6 x = .827
6 x = 6.1729
x = 1.0288

Answer 7

or, for #1, just change the base to one you know

log_5(14) = log14/log5 = 1.64
now you are already at
2x-9 = 1.64

Answer 8

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