im a little confused how to find a solution please read the equation closely.....

Question

What is the value of x in the logarithmic equation:

log₃√3 + log_x(1/25) + log_a1 - log_mm = -3.5

Answer 1

All terms are based on the basic laws of logarithms. Learn them.

log₃ √3 = 0.5

log_a 1 = 0

log_m m = 1

0.5 + log_x (1/25) + 0 - 1 = -3.5

log_x (1/25) = -3

x^-3 = 0.04

1 / x³ = 0,04

1 = 0.04x³

25 = x³

³√25 = x

Answer 2

log₃√3 = log₃3^1/2 = 1/2log₃3 = 1/2

log_a1 = 0 (because a⁰ = 1)

log_mm = 1 (because m¹ = m)

So:

log₃√3 + log_x(1/25) + log_a1 - log_mm = -3.5

1/2 + log_x(1/25) + 0 - 1 = -3.5

log_x(1/25) = -3

x^-3 = 1/25

1/x³ = 1/25

x³ = 25

x = cuberoot(25)