Question

NEED HELP ASAP WILL MARK BRAINLIEST!

Answer 1

Answer:

$\boxed {1)log_{b}(75) = 4.317}$

$\boxed {2)ln(20) = 2.9957}$

Step-by-step explanation:

$\textsf {Question l :}$

$\longrightarrow \mathsf {log_{b}(3) = 1.099}$

$\longrightarrow \mathsf {log_{b}(5) = 1.609}$

$\textsf {Identities applied :}$

$\boxed {log(ab) = loga + logb}$

$\boxed {log(a)^{x} = xloga}$

$\textsf {We can rewrite the problem as :}$

$\longrightarrow \mathsf {log_{b}(75)}$

$\longrightarrow \mathsf {log_{b}(25 \times 3)}$

$\longrightarrow \mathsf {log_{b}(5^{2} \times 3)}$

$\longrightarrow \mathsf {log_{b}(5)^{2} + log_{b}(3)}$

$\longrightarrow \mathsf {2log_{b}(5) + log_{b}(3)}$

$\textsf {Now, substitute the values :}$

$\longrightarrow \mathsf {2(1.609) + (1.099)}$

$\longrightarrow \mathsf {3.218 + 1.099}$

$\longrightarrow \mathsf {4.317}$

$\boxed {log_{b}(75) = 4.317}$

$\textsf {Question ll :}$

$\longrightarrow \mathsf {ln(4) = 1.3863}$

$\longrightarrow \mathsf {ln(5) = 1.6094}$

$\textsf {Rewriting the problem :}$

$\longrightarrow \mathsf {ln(20)}$

$\longrightarrow \mathsf {ln(4 \times 5)}$

$\longrightarrow \mathsf {ln(4) + ln(5)}$

$\longrightarrow \mathsf {1.3863 + 1.6094}$

$\longrightarrow \mathsf {2.9957}$

$\boxed {ln(20) = 2.9957}$

Answer 2

Answer:

$\sf \log_b(75)=4.317$

$\sf \ln (20)=2.9957$

Step-by-step explanation:

Question 1

Given:

  $\sf \log_b(3)=1.099$

  $\sf \log_b(5)=1.609$

To evaluate $\sf \log_b(75)$,  replace 75 with (5 × 5 × 3):

$\implies \sf \log_b(5 \cdot 5 \cdot 3)$

$\textsf{Apply the Product log law}: \quad \log_axy=\log_ax + \log_ay$

$\implies \sf \log_b5+\log_b5+\log_b3$

Substitute the given values to solve:

$\implies \sf 1.609 + 1.609 + 1.099=4.317$

Question 2

Given:

  $\sf \ln(4)=1.3863$

  $\sf \ln(5)=1.6094$

To evaluate ln(20) replace 20 with (4 × 5):

$\implies \sf \ln (4 \cdot 5)$

$\textsf{Apply the Product log law}: \quad \ln xy=\ln x + \ln y$

<em />$\implies \sf \ln (4)+\ln (5)$

Substitute the given values to solve:

$\implies \sf 1.3863+1.6094=2.9957$