Question

Solve to find x log (3x+5) to base 5= 2log (1-3x) to base 25

Answer 1

Answer:

x = -2/ 3

Step-by-step explanation:

in order to cancel out the logs they should have common bases

$\mathsf{ log_{5}(3x + 5) = 2 log_{25}(1 - 3x) }$

we can write 25 as 5²

$\mathsf{ \implies log_{5}(3x + 5) = 2 \: log_{ {5}^{2} }(1 - 3x) }$

we know that the reciprocal of the exponents of the bases are multiplied to the log

$\mathsf{ \implies log_{5}(3x + 5) = \frac{1}{\cancel{2} } \times \cancel{2} \: log_{ 5}(1 - 3x) }$

and now since the logs have common bases

$\mathsf{ \implies \cancel { log_{5}}(3x + 5) = \cancel{ log_{ 5}}(1 - 3x) }$

we're left with

$\mathsf{ \implies 3x + 5 = 1 - 3x}$

$\mathsf{ \implies 9x = -4}$

x = -2/ 3