Question

pls help me thank you .....​

Answer 1

Step-by-step explanation:

log15√5 + log3√5 = 2

log(18√5)=2

18√5= x^2

x = 6.34

Answer 2

Given:-

• $\sf log_{x}(15 \sqrt{5} ) = 2 - log_{x}(3 \sqrt{5} )$

To find:-

• The value of x

Answer:-

Given that,

$\sf log_{x}(15 \sqrt{5} ) = 2 - log_{x}(3 \sqrt{5} )$

$\sf \longrightarrow log_{x}(15 \sqrt{5} ) + log_{x}(3 \sqrt{5} ) = 2$

${\blue{\bigstar}} \boxed{\sf{log_a (p) + log_a (q) = log_a(pq)}}$

$\sf \longrightarrow log_{x}(15 \sqrt{5} \times 3 \sqrt{5} ) = 2$

$\sf \longrightarrow log_{x}(225) = 2$

Writing in exponential form,

$\sf \longrightarrow {x}^{2} = 225$

$\sf \longrightarrow x = \pm 15$

But $\sf x$ is the base of a logarithm such as $\sf log_x(15\sqrt{5})$ or $\sf log_x(3\sqrt{5})$. And since the base of a logarithm can't be negative, we will consider only positive value.

$\longrightarrow \underline{\underline{\sf{ \green{ x = 15 } }}}$