Question

log0.7log4 (x-5) = 0
with an explanation please)

Answer 1

ODZ: The sublogarithmic expression must be greater than 0. We have a logarithm inside the logarithm, so the internal logarithm must be greater than 0.

log₄ (x - 5)> 0;

log₄ (x - 5)> log₄1

x - 5> 1

x> 6

x - 5> 0

x> 5

=> x ∈ (6; + ∞)

log0.7 (log₄ (x - 5)) = 0

log0.7 (log₄ (x - 5)) = log0.7 (1)

log₄ (x - 5) = 1

log₄ (x - 5) = log₄4

x = 5 = 4

x = 9 is the root of DD =>.

Answer: 9.