Question

How do you solve the question 10^x+2 = 20^x+1. The carrot means to the power of and everything that comes after it. When the equal sign comes that's the other side of the equation

Answer 1

Answer:

x=0.3

Step-by-step explanation:

we can organize the equation in a convenient form and to simplify

$10^{x+2}=20^{x+1}\\10^{x}*10^{2}=20^{x}*20\\100*10^{x}=20*2^{x}*10^{x}\\100=20*2^{x}\\50=2^{x}$

now we can apply log in base 2 to get x

$log_{2}(50)=log_{2}(2^{x})\\\\\frac{log(50)}{log(2)}=x\\\\x=0.30$

where we have used that

$log_{a}(b)=\frac{log(b)}{log(a)}$

I hope this is useful for you

regards