Question

15points question fasstt

Answer 1

$\sf{2^{n-5}\cdot \:5^{n-4}=5}$

• Apply Exponent Rule : $\sf{a^{b+c}=a^b\cdot a^c}$

$\to\sf{2^{n-5}\cdot \:5^{n-5}\cdot \:5^1=5}$

• Apply Exponent Rule : $\sf{a^cb^c=(ab)^c}$

$\to\sf{10^{n-5}\cdot \:5^1=5}$

$\to\sf{10^{n-5}\cdot \:5=5}$

• Dividing Both Sides by 5

$\to\sf{10^{n-5}=1}$

• If $\sf{f(x)=g(x)}$ , then $\sf{\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)}$

$\to\sf{\ln \left(10^{n-5}\right)=\ln \left(1\right)}$

• Apply Log Rule : $\sf{\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)}$

$\to\sf{\left(n-5\right)\ln \left(10\right)=\ln \left(1\right)}$

• Dividing Both Sides by $\sf{\ln \left(10\right)}$

$\to\sf{n-5=0}$

• Adding 5 to both Sides

$\to\sf{n-5+5=0+5}$

$\to\sf{n=5}$

Answer 2

Answer:

First Answer is the correct answer.