# Thread: Did I solve these logarithms correctly?

1. ## Did I solve these logarithms correctly?

1. 35log[base 6](x) = 18
My answer: x = 6^18/35

2. 6^(-0.2x) - 3 = 7
A bit stuck on this one. I get as far as 6^(-0.2x) = 9, but I'm a bit lost at finding the x?

3. 7log[base 5](x) - 3 = 15
My answer: x = 5^12/7

2. 1. is correct.

2. is incorrect

$6^{-0.2x} - 3 = 7$

$6^{-0.2x} = 10$

$-0.2x = \log_6{10}$

$x = -5\log_6{10}$.

3. is also wrong.

$7\log_5{x} - 3 = 15$

$7\log_5{x} = 18$

$\log_5{x} = \frac{18}{7}$

$x = 5^{\frac{18}{7}}$.