BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

If \(5^x-5^{x-3}=124\cdot 5^y,\) what is \(y\) in terms of \(x?\)

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

Re: If \(5^x-5^{x-3}=124\cdot 5^y,\) what is \(y\) in terms of \(x?\)

by deloitte247 » Fri Nov 06, 2020 3:04 pm
$$5^x-5^{\left(x-3\right)}=124\cdot5^y$$
$$5^x\left(1-5^{-3}\right)=124\cdot5^y$$
$$5^x\left(1-\frac{1}{5^3}\right)=124\cdot5^y$$
$$5^x\left(1-\frac{1}{125}\right)=124\cdot5^y$$
$$\frac{5^x\left(125-1\right)}{125}=124\cdot5^y$$
$$5^x=5^3\cdot125$$
$$5^x=5^3\cdot5^3$$
$$5^x=5^{\left(y+3\right)}$$ $$x=y+3$$
$$x=y+3$$
$$y=x-3$$

$$ption\ is\ Option\ C$$
Top
Post new topic Post Reply
• Page 1 of 1