## Nick88888888 one year ago (1.05)^x = 2.5 Round your answer to the nearest tenth. how would i do this step by step? 2. ___ √ 3x = 50 Round your answer to the nearest tenth.

1. anonymous

Apply logarithm of base 10 to both the sides $\log_{10}((1.05)^{x})=\log_{10}(2.5)$ Rule: 1.$\log(x^y)=y.\log(x)$ (true for all base) 2.$\log_{a}a=1$ log of any number to it's base is 1 3.$\log(a \times b)=\log(a)+\log(b)$ 4.$\log(\frac{a}{b})=\log(a)-\log(b)$ Also true for all base 5.$\log(1)=0$ Also true for all base $x.\log_{10}(1.05)=\log_{10}(\frac{10}{4})$ Here's the first I've applied property 1 to left side and written right side 2.5 as 10/4 use property 4 on right side now Note on the right side I've written 2.5 as 10/4

2. Nick88888888

Ok so i just do (1.05)(10/4) or... what

3. anonymous

4. anonymous

ok Consider an example $(0.4)^x=\frac{0.25}{100}$ Apply log of base 10 to both sides $\log_{10}(0.4)^x=\log_{10}(\frac{0.25}{100})$ Use rule 1 on left side and rule 4 on right side $x.\log_{10}(0.4)=\log_{10}(0.25)-\log_{10}(100)$ Now we can write 0.4 as 4/10 0.25 as square of 0.5 and 100 as square of 10 so do that $x.\log_{10}(\frac{4}{10})=\log_{10}((0.5)^2)-\log_{10}(10^2)$ Property 4 on left and property property 1 on right $x[\log_{10}(4)-\log_{10}(10)]=2\log_{10}(0.5)-2\log_{10}(10)$ We can write 4 as 2 square and 0.5 as 1/2 so do that $x[\log_{10}(2^2)-\log_{10}(10)]=2[\log_{10}(\frac{1}{2})-\log_{10}(10)]$ Use properties to simplify further $x[2\log_{10}(2)-\log_{10}(10)]=2[\log_{10}(1)-\log_{10}(2)-\log_{10}(10)]$ Now put the values in, $\log_{10}(2)=0.3010$ By property 2 and property 5 the other values are $\log_{10}(10)=1$$\log_{10}(1)=0$$x[2 \times 0.3010-1]=2[0-0.3010-1]$$-0.398x=-2.06$$x=\frac{2.06}{0.398}\approx 5.176$

5. Nick88888888

sorry didnt mean to bump