This is quite a difficult question to answer fully, because rocket science is hard.
There are three things you need to do.
- Boost your rocket high enough that it leaves the atmosphere so you can enter a suitable orbit (I'll ignore boosting straight into an escape trajectory for now).
- Boost your rocket out quickly enough that you don't spend more time (and hence fuel) fighting against the force of gravity than you really need to. This is called gravity drag.
- Boost your rocket out of the thickest part of the atmosphere as quickly as possible so as to avoid waisting fuel pushing through the atmosphere (atmospheric drag), but not so fast that the dynamic pressure your rocket experiences smashes it to bits (Max q).
Part (1) might actually be easier on your super-earth... the scale height of the atmosphere is inversely proportional to the strength of the planetary gravity, so for the same surface temperature the scale height will be smaller as gravity is smooshing the atmosphere into a thinner layer. Surface air pressure will be higher, but the thickest part of the atmosphere will be thinner, making (3) hard to work out.
For a 200km orbit on earth, you need an orbital velocity of about 7.8km/s. Actual rockets need a delta-V budget about 1.5km/s higher than this as a result of those gravity drag and atmospheric drag losses.
Assuming your planet has the same average density to Earth, it'll have a 50% greater radius and hence have about 3.4x Earth's mass. Orbital velocity at 200km is, surprise! about 1.5x the velocity at the same altitude on earth.
Lets be optimistic and assume that the additional atmospheric and gravity drag losses are also 1.5x their terran equivalent. You'll therefore need a delta-V budget of about 14km/s, which is about 4.7km/s bigger than that required on Earth. This is a punishing amount extra. From the rocket equation, $\Delta_v = v_e\log{(m_0/m_f)}$, where $v_e$ is the rocket exhaust velocity, $m_0$ is the fully fuelled and ready to go rocket mass and $m_f$ is the final empty mass of the rocket (or dry mass). For the same rocket technology, you either need to double the amount of fuel in your rocket (without increasing the empty mass of the rocket!), or halve the weight of your rocket and its payload (and still carry the same amount of fuel!). You'll also need 50% more thrust to maintain the same sort of trajectory... anything less than that and your gravity losses mount up rapidly as you'll be spending much longer trying to thrust up using your weedy rockets.
If you could handwave the issue of thrust away, and reduce your problem to one of delta-V, then you could just throw in an extra stage by taking a really, really big rocket design and replacing its intended payload with another rocket.
The Sea Dragon (as suggested by Zeiss Ikon in the OP comments) can lift a substantial 550 tonnes to LEO. The Delta-IV Common Booster Core has a fuelled mass of about 232 tonnes and an empty mass of about 28 tonnes. Given the performance of its rocket engine (full specs here) it could be strapped to a 65 tonne payload and have a delta-V of about 4.7km/s. If you were able to scale that design up linearly, which seems plausible, you'd be able to push about 120 tonnes into orbit using that super-CBC as a third stage using to all the 550kg payload available with the Sea Dragon. Your rocket's launch weight is about 18000 tonnes, giving it a mass ratio of about 1:150.
Handwaving the issue of thrust away isn't really something you'll find you're able to do in the real world. Rocket thrust is defined as $F = \dot{m} v_e$, where $\dot{m}$ is the mass of fuel you're throwing through the engine per second, and $v_e$ is the exhaust velocity. You can trivially increase thrust by adding extra rocket engines... but now you're burning through your fuel much more quickly so you have to carry more fuel, and your dry mass has gone up which reduces your stage's delta-V (because the rocket equation ruins everything) and so on and so forth. Complex staging mechanisms are the solution in Kerbal Space Program, but they're tricky to implement in the real world... SpaceX recently cancelled their fuel-crossfeed project for example, at least in part because the engineering is Quite Hard.
That just leaves you increasing your exhaust velocity. You can't really do that with a chemical rocket, because the liquid hydrogen/liquid oxygen combination is about as good as it gets. If you want an engine that shoots stuff out faster and provides the sort of massive thrust you'll need to efficiently escape your super earth, you're almost certainly going to have to take the Nuclear Option.
Now, nuclear rockets have been built in the past and even operated from static test cells, though none have ever actually lifted off. That puts them at the edge of plausibility for "technology we currently have", but these things aren't vapourware or handwavium. According to Project Rho, the Dumbo Nuclear Thermal Rocket looks like it has the sort of outrageous thrust-to-weight ratio and specific impulse that you need. With a bunch of those, the Sea Dragon/CBC couple become a 3-stage nuclear rocket, littering the world below it with spent fuel rods as it headed for the stars, but it would be able to get there and carry a decent amount of stuff with it.
So there you go. Pure chemical rocket? Tenuous. Nuclear rocket? Probably fine.