First of all - these are all really good - a great job, well done.
I searched for these icons, and they are similar but none I could find the same - so again well done for being unique. The amount of people that come here using stock images as logos is crazy.
Here’s a few snippets I took from what you posted - and my initial response.
And then a more thought out process below.
Your taste doesn’t come into the equation
No idea what the text is - and I can’t read the text so it doesn’t speak to what the company is.
Lots of logos don’t, Coke, Nike, Google, Adidas - but they are established brands with world wide recognition. Apple for example, they had a crappy logo at the start, but built a reputation on computers and then simplified it over time.
Yours is modern and abstract (to extents)
Not good. You shouldn’t undersell yourself.
This type of deal should come with very limited revisions and time spent.
50% upfront for unknown clients (non refundable)
Don’t give away your skills.
He runs a laboratory that charges fees for tests.
Would they do you a favour cos you’re a friend of their friend? Would they lower their fees for you?
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What other types of equipment do they use?
I know when I bring my dog for a urine test at the Vet - they require me to bring him outside and fill a cup with his pee.
And I’d imagine humans would associate filling a cup with Pee would also be the same for animals for testing.
Maybe it’s simpler than you think.
Here’s my more in-depth thoughts.
Understand the client and their vision. You’ve emphasised the microscope but it’s sub to the name of the lab or at least equal value - what I gather is they want the microscope to be the main image - and not modern. They want probably premodern maybe a more of a handdrawn feel.
Get moodboards and think of different design directions - show the client various styles/colours/approaches. Get them to tell you what they like/don’t like from the different moodboards.
Show other logos you have designed and the design process in them and why they work - it might help them understand your approach is actually good and open their eyes a little to a different approach.
I said earlier your style shouldn’t come into it. That’s not entirely true - you should of course compromise without compromising quality. It’s always a case of finding a middle ground - which usually means incorporating elements they like that you may not like.
And set your boundaries. It might be a low budget, but it’s not unlimited revisions and you should have this already agreed. You should be compensated fairly for your time.
If it’s not working - you can walk away - but hope you got 50% or some payment upfront - that’s usually what I would do if working with an unknown client.
It’s ok to tell them that it’s not realistic to be achieved in the budget and timeframe. It’s ok to say you need to charge more based on certain circumstances. It’s managing expectations.
Keep it professional, patient, and show your commitment to finding a solution that suits. But the budget is the budget and if they reach the budget amount and not willing to budge, then neither should you.
It’s ok to wait for them to come to senses.
Don’t undersell yourself.
